You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB is the diameter of circle O, CD is a chord of circle O, and ∠ABD = 60°. What is the measure of ∠C?
(A) 15°
(B) 30°
(C) 45°
(D) 60°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, AB is the diameter of circle O, points C and D are on circle O. If ∠C = 40°, what is the degree measure of ∠ABD?
Choices:
(A) 40°
(B) 50°
(C) 80°
(D) 90°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, PA and PB are tangents to circle O, with points A and B as the points of tangency. Point C lies on circle O, and angle ACB is 56°. What is the measure of angle APB?
Choices:
(A) 58°
(B) 68°
(C) 78°
(D) 124°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, circle O is the circumcircle of triangle ABC. If OA and OB are connected and angle AOB is 80°, what is the degree measure of angle C?
Choices:
(A) 30°
(B) 40°
(C) 50°
(D) 80°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the right triangle ABC shown in the figure, where ∠A = 25° and ∠ACB = 90°, a circle with center C and radius BC intersects AB at point D and AC at point E. What is the measure of angle DCE?
Choices:
(A) 30°
(B) 25°
(C) 40°
(D) 50°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Given that each pair of polygons is similar, what is the value of x?
Choices:
(A) 29
(B) 55.3
(C) 71.05
(D) 78

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In triangle ABC, which is an isosceles triangle with base BC, what is the perimeter of the triangle?
Choices:
(A) 5
(B) 12
(C) 14
(D) 40

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of y, assuming that segments that seem to be tangent are indeed tangent. Round your answer to the nearest tenth if needed. What is the value of y?
(A) 10.6
(B) 11.6
(C) 12.6
(D) 13.6

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the measure of angle 2.
Choices:
(A) 28
(B) 38
(C) 52
(D) 62

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Given that in the figure, the measure of angle 1 is 58 degrees, angle 2 is 47 degrees, and angle 3 is 26 degrees, what is the measure of angle 7?
Choices:
(A) 47
(B) 49
(C) 58
(D) 73

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of y in the given figure.
Options:
(A) 20
(B) 30
(C) 40
(D) 50

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, in quadrilateral ABCD, AC and BD intersect at point O, with OE perpendicular to BD and intersecting AD at point E. If the perimeter of quadrilateral ABCD is 20, what is the perimeter of triangle ABE?
Choices:
(A) 4
(B) 6
(C) 8
(D) 10

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In triangle ABC, where angle C is 90 degrees, sin A = 4/5, and BC = 12, what is the length of AC?
(A) 3
(B) 9
(C) 10
(D) 15

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, if the diameter AB of circle O forms an angle of 35° with chord AC, and the tangent PC passing through point C intersects the extension of AB at point P, what is the measure of angle ∠P?
Choices:
(A) 15°
(B) 20°
(C) 25°
(D) 30°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, it is known that line AD is a tangent to circle O with point A as the point of tangency. Point D lies on circle O and intersects circle O at point B. Point C is on circle O, and angle ODA is 36°. What is the degree measure of angle ACB?
Choices:
(A) 54°
(B) 36°
(C) 30°
(D) 27°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In triangle ABC, point D and E are the midpoints of BC and AD respectively. If EF = 2FC and the area of triangle ABC is 12, what is the area of triangle BEF?
Choices:
(A) 5
(B) 4.5
(C) 4
(D) 3.5

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, quadrilateral ABCD is inscribed in circle O. If ∠B = 130°, what is the measure of ∠AOC?
Choices:
(A) 130°
(B) 120°
(C) 110°
(D) 100°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the measure of angle B.
Choices:
(A) 90
(B) 180
(C) 270
(D) 360

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In parallelogram PQRS, ST is equal to TR. What is the ratio of the area of triangle QST to the area of the parallelogram PQRS?
Choices:
(A) 1:2
(B) 1:3
(C) 1:4
(D) 1:5
(E) it cannot be determined

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, one edge of the ruler passes through a right angle vertex, and the other edge of the ruler intersects with one side of the right angle. If ∠1 = 30°, what is the degree measure of ∠2?
Choices:
(A) 30°
(B) 45°
(C) 60°
(D) 120°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, if BD = 120m, DC = 60m, and EC = 50m, what is the width of the river AB?
Choices:
(A) 120m
(B) 100m
(C) 75m
(D) 25m

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of z.
Options:
(A) 2√5
(B) 2√6
(C) 2√10
(D) 2√15

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the parallelogram ABCD, if the sum of angles A and C is 160°, what is the degree measure of angle B?
Choices:
(A) 100°
(B) 80°
(C) 60°
(D) 20°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In parallelogram ABCD, diagonal AC intersects diagonal BD at point O, with AB perpendicular to AC. If CD = 8 and AC = 12, what is the length of DB?
Choices:
(A) 20
(B) 18
(C) 16
(D) 10

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure shown, with line a parallel to line b, angle 2 is 28° and angle 1 is 50°. What is the measure of angle A?
Choices:
(A) 32°
(B) 78°
(C) 22°
(D) 20°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, it is known that line a is parallel to b and c, and lines m and n intersect a, b, and c at points A, C, E, B, D, F respectively. If AC = 8, CE = 12, and BD = 6, what is the value of BF?
Choices:
(A) 14
(B) 15
(C) 16
(D) 17

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, PQ, PR, and AB are tangents to circle O, with points Q, R, and S as the points of tangency. If ∠APB = 40°, what is the measure of ∠AOB?
(A) 40°
(B) 50°
(C) 60°
(D) 70°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In triangle ABC, BC = 3. Point D is on the extension of AC, such that AC = 3CD. Line DH is drawn parallel to AB passing through point D, intersecting the extension of BC at point H. If ∠CBD = ∠A, what is the length of AB?
Choices:
(A) 6
(B) 5
(C) 4
(D) 4.2

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the precise circumference of the circle.
Options:
(A) 17π
(B) 30π
(C) 34π
(D) 64π

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the circle O, chord AC is 7 units long, chord AE is perpendicular to radius OB with a length of 24 units, and angle CAO is equal to angle BOA. What is the radius of circle O?
(A) 12
(B) 12.5
(C) 13
(D) 14

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If the measure of angle DGF is 53 degrees and the measure of angle AGC is 40 degrees, what is the measure of angle 1?
(A) 37
(B) 40
(C) 50
(D) 53

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

What is the degree measure of angle 1 when a set square is positioned on a ruler as shown in the diagram?
Choices:
(A) 95°
(B) 100°
(C) 105°
(D) 110°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, AD is parallel to BE which is parallel to CF. Lines l1 and l2 intersect these three parallel lines at points A, B, C and points D, E, F respectively. If DE = 6, what is the value of DF?
Choices:
(A) 4
(B) 9
(C) 10
(D) 15

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, AB is the diameter of circle O, CD is a chord of circle O, and AC, AD, BD are connected. If ∠CAB = 35°, what is the measure of ∠ADC?
Choices:
(A) 35°
(B) 55°
(C) 65°
(D) 70°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, the radius of circle O is 2, triangle ABC is an inscribed triangle of circle O, and OB, OC are connected. If ∠BAC and ∠BOC are complementary, what is the length of chord BC?
Choices:
(A) √{3}
(B) 2√{3}
(C) 2√{2}
(D) 4

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Given that the measure of angle 1 is 53 degrees in the figure, what is the measure of angle 6?
Choices:
(A) 53
(B) 57
(C) 63
(D) 67

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, quadrilateral ABCD is inscribed in circle O, with angle BOD measuring 130°. What is the degree measure of angle BCD?
Choices:
(A) 50°
(B) 125°
(C) 115°
(D) 150°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the rhombus ABCD, points M and N are located on sides AB and CD respectively, with AM equal to CN. Line MN intersects AC at point O, and line BO is drawn. If angle DAC is 36°, what is the measure of angle OBC?
(A) 34°
(B) 54°
(C) 62°
(D) 72°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given figure, AB is parallel to DF, AC is perpendicular to CE at C, and BC intersects DF at point E. If ∠A = 20°, what is the measure of ∠CEF?
Choices:
(A) 110°
(B) 100°
(C) 80°
(D) 70°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB is the diameter of circle O, ∠ADC = 30°, OA = 2. What is the length of BC?
Choices:
(A) 2
(B) 4
(C) 2√{3}
(D) √{3}

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB is the diameter of circle O, and C, D are two points on circle O. If ∠D = 56°, what is the degree measure of ∠ABC?
Choices:
(A) 37°
(B) 34°
(C) 35°
(D) 36°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If in circle A, WX = XY = 22, what is the value of AB?
Choices:
(A) 5
(B) 10
(C) 11
(D) 22

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB is the diameter of circle O, point C lies on the circumference, BC and OC are connected, and AD is drawn parallel to OC passing through point A to intersect circle O at point D. If ∠B = 25°, what is the degree measure of ∠BAD?
Choices:
(A) 25°
(B) 30°
(C) 40°
(D) 50°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, circle O is tangent to line AB at point A. Line BO intersects circle O at point C, and angle BAC is 30°. What is the measure of angle B?
Choices:
(A) 20°
(B) 30°
(C) 50°
(D) 60°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, it is known that the equilateral triangle ABC has a side length of 9. Point P is on BC such that BP = 3, and point D is on AC where ∠APD = 60°. What is the length of segment CD?
Choices:
(A) 1
(B) 2
(C) 3
(D) 4

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If the measure of angle GH is 78 degrees, what is the measure of angle 2?
(A) 39
(B) 51
(C) 78
(D) 114

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, point P lies on the diagonal AC of the rhombus ABCD, where AB = 2cm and ∠B = 120°. Point E is the perpendicular projection of P onto CD, and point F is the perpendicular projection of P onto AD. What is the value of PE + PF?
Choices:
(A) √{2}
(B) √{3}
(C) 2
(D) \frac{3√{2}}{2}

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB is the diameter of circle O, chord CD is perpendicular to AB, and chord AF is extended. If ∠DFC = 48°, what is the degree measure of ∠CFE?
Choices:
(A) 60°
(B) 66°
(C) 68°
(D) 72°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Calculate the area of the shaded sector and round to the nearest tenth.
Choices:
(A) 1.5
(B) 2.2
(C) 3.8
(D) 5.3

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, triangle ABC is inscribed in circle O, with angle A measuring 60°. What is the measure of angle BOC?
Choices:
(A) 30°
(B) 120°
(C) 110°
(D) 100°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the measure of angle D.
Choices:
(A) 117
(B) 117
(C) 126
(D) 127

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, quadrilateral ABCD is inscribed in circle O. Given that angle BCE is 70°, what is the degree measure of angle A?
Choices:
(A) 110°
(B) 70°
(C) 55°
(D) 35°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Rectangle ABCD has a perimeter of 26, and the half circle with diameter AD has an area of 8*pi. What is the perimeter of the unshaded part of the figure?
Choices:
(A) 26+4*pi
(B) 18+8*pi
(C) 18+4*pi
(D) 14+4*pi
(E) 14+2*pi

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, a ramp is 130m long, with the top of the ramp 50m above the horizontal ground. What is the tangent value of the angle between the ramp and the horizontal ground?
Choices:
(A) \frac{5}{13}
(B) \frac{12}{13}
(C) \frac{5}{12}
(D) \frac{13}{12}

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, OE is the bisector of ∠AOB, CD is parallel to OB intersecting OA at C and OE at D, ∠ACD is 50°. What is the measure of ∠CDO in degrees?
Choices:
(A) 15°
(B) 20°
(C) 25°
(D) 30°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, points A, B, and C lie on circle O, with angle ABC measuring 30°. What is the measure of angle OAC?
Choices:
(A) 60°
(B) 45°
(C) 35°
(D) 30°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, two lines a and b intersect at point O. If angle 1 is 60°, what is the measure of angle 2?
Choices:
(A) 50°
(B) 60°
(C) 110°
(D) 120°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB is the diameter of circle O, C is a point on circle O, and a tangent to circle O passing through point C intersects the extension of AB at point D. If ∠A = 30°, what is the measure of ∠D?
Choices:
(A) 30°
(B) 60°
(C) 40°
(D) 25°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the rhombus ABCD shown in the figure, if ∠ABC = 60° and AC = 6, what is the length of AB?
(A) 10
(B) 6
(C) 3
(D) Cannot be determined

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, A and D are two points on the circle O, with BC as the diameter. If ∠D = 35°, what is the measure of ∠OAC?
Choices:
(A) 65°
(B) 35°
(C) 70°
(D) 55°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of x.
Options:
(A) 7
(B) 8
(C) 11
(D) 13

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of y.
Options:
(A) 6
(B) 8
(C) 10
(D) 12

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given figure, the base BC of isosceles triangle ABC is 6 units long, with an area of 36 square units. The perpendicular bisector EF of the base AC intersects sides AC and AB at points E and F, respectively. If point D is the midpoint of side BC and point M is a moving point on segment EF, what is the minimum perimeter of triangle CDM?
Choices:
(A) 6
(B) 10
(C) 15
(D) 16

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Given that Q R \parallel T S, Q T \parallel R S, and m \angle 1 = 131 in the figure, what is the measure of \angle 8?
Choices:
(A) 101
(B) 111
(C) 121
(D) 131

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, the radius of circle O is 1. Line PA is tangent to circle O at point A, and lines OA and OP intersect circle O at point D, with angle APO measuring 30°. Chord AB is perpendicular to OP at point C. What is the area of the shaded region in the diagram?
Choices:
(A) π/6
(B) π/3
(C) π/2
(D) √3/2 * π

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given figure, it is known that the hypotenuse AB of right triangle ABC is 13cm and one leg AC is 5cm. If a cone is formed by rotating line BC around as an axis, what is the surface area of this cone in square centimeters?
Choices:
(A) 65π
(B) 90π
(C) 156π
(D) 300π

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, a rectangular paper ABCD is folded along the diagonal BD, resulting in point C coinciding with point E. Connecting BE intersects AD at F. Folding triangle DEF along DF results in point E coinciding with point G. If DG precisely bisects angle ADB, what is the degree measure of angle ADB?
Choices:
(A) 18°
(B) 20°
(C) 36°
(D) 45°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of x, assuming that segments that seem to be tangent are indeed tangent.
Choices:
(A) 3
(B) 9
(C) 12
(D) 15

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, points A, B, C, and D are on circle O, with CD perpendicular to AB at E. If angle ADC is 50°, what is the measure of angle BCD?
Choices:
(A) 50°
(B) 40°
(C) 30°
(D) 25°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given figure, point C lies on the circle O. If the central angle ∠ACB is 36°, what is the degree measure of the central angle ∠AOB?
Choices:
(A) 18°
(B) 36°
(C) 54°
(D) 72°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, if ∠1 is equal to ∠2, and ∠D is 78°, what is the measure of ∠BCD?
(A) 98°
(B) 62°
(C) 88°
(D) 102°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, it is given that AB is parallel to CD, AC is equal to BC, and if angle 1 is 70°, what is the degree measure of angle 2?
Choices:
(A) 40°
(B) 45°
(C) 50°
(D) 55°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB and AC are tangents to circle O, with points of tangency at B and C. Point D lies on minor arc BC. If ∠BAC = 80°, what is the measure of ∠BDC in degrees?
Choices:
(A) 50
(B) 80
(C) 100
(D) 120

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Given that m∠1 = 4p + 15, m∠3 = 3p - 10, and m∠4 = 6r + 5 in the figure, what is the value of r?
Choices:
(A) 10
(B) 15
(C) 20
(D) 25

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, if the slant height of a cone is 10 and the diameter of its base circle is 12, what is the lateral surface area of this cone?
Choices:
(A) 24π
(B) 30π
(C) 48π
(D) 60π

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, AD is parallel to BE and CF, and lines a, b intersect these three parallel lines at points A, B, C and points D, E, F respectively. If AB = 4, BC = 6, and DE = 3, what is the length of EF?
Choices:
(A) 4
(B) 5
(C) 6
(D) 4.5

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, quadrilateral ABCD is inscribed in circle O. Given that angle BCE is 70°, what is the degree measure of angle A?
Choices:
(A) 110°
(B) 70°
(C) 55°
(D) 35°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of M N in triangle J M N, which is an isosceles triangle with J M congruent to M N.
Choices:
(A) 2
(B) 3
(C) 4
(D) 5

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, the vertices A, B, D of parallelogram ABCD lie on circle O, with vertex C on diameter BE. If ∠ADC = 54° and AE is connected, what is the measure of ∠AEB?
Choices:
(A) 36°
(B) 46°
(C) 27°
(D) 63°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, triangle ABC is inscribed in a circle. Point D lies on BC, and angle B is folded along AD such that point B coincides with point E on the circle. If angle C is 50°, what is the measure of angle BAE?
Choices:
(A) 40°
(B) 50°
(C) 80°
(D) 90°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, two concentric circles have radii of 3cm and 5cm respectively. Chord AB is tangent to the smaller circle at point C. What is the length of AB?
Choices:
(A) 4cm
(B) 5cm
(C) 6cm
(D) 8cm

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the measure of angle F.
Choices:
(A) 102
(B) 107
(C) 112
(D) 122

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If the measure of angle JH is 114 degrees, what is the measure of angle 3?
Choices:
(A) 33
(B) 43
(C) 57
(D) 67

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the measure of angle ZXY.
Choices:
(A) 25
(B) 65
(C) 115
(D) 180

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, the vertical height of a slope is 300m, and the length of the slope is 500m. What is the gradient of this slope?
Choices:
(A) 0.6
(B) 0.75
(C) 0.8
(D) Cannot be determined

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, points A, B, and C are all on circle O. If ∠C = 40°, what is the degree measure of ∠AOB?
Choices:
(A) 40°
(B) 50°
(C) 80°
(D) 140°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, triangle ABC is inscribed in circle O, with AD perpendicular to BC at point D, and BE perpendicular to AC at point E. AD and BE intersect at point H. If BC = 6 and AH = 4, what is the radius of circle O?
Choices:
(A) 5
(B) 2√{13}
(C) √{13}
(D) 5.5

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, line AB intersects line CD at point O, with OE perpendicular to CD at point O. If ∠AOC = 52°, what is the degree measure of ∠BOE?
Choices:
(A) 142°
(B) 128°
(C) 148°
(D) 152°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, ⊙O is the circumcircle of △ABC, with ∠BAC = 60°. If the radius OC of ⊙O is 2, what is the length of chord BC?
Choices:
(A) 4
(B) 2√{3}
(C) 3
(D) √{3}

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, which represents the famous ancient Chinese "Zhao Shuang Xian Diagram", it is composed of four congruent right-angled triangles. If AE=10 and BE=24, what is the length of EF?
Choices:
(A) 14
(B) 13
(C) 14
(D) 14

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In parallelogram JKLM, if JK is equal to 2b + 3 and JM is equal to 3a, what is the value of b?
Choices:
(A) 7
(B) 14
(C) 21
(D) 45

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, A, B, and C are three points on circle O with a radius of 1. If AB = √2 and ∠CAB = 30°, what is the degree measure of ∠ABC?
Choices:
(A) 95°
(B) 100°
(C) 105°
(D) 110°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, ⊙O is the circumscribed circle of regular hexagon ABCDEF, and P is a point on arc AB. What is the degree measure of ∠CPD?
Choices:
(A) 30°
(B) 40°
(C) 45°
(D) 60°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Given that F K = 3x - 1, K G = 4y + 3, J K = 6y - 2, and K H = 2x + 3, determine the value of y that would make the quadrilateral a parallelogram. Which of the following choices is the correct value of y?
(A) 1
(B) 2.5
(C) 3
(D) 5

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, it is known that line AB is parallel to CD, angle C is 80°, and angle A is 40°. What is the measure of angle E?
Choices:
(A) 80°
(B) 30°
(C) 40°
(D) 60°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If a right-angled triangle board is arranged as shown in the figure, where ∠C=90°, ∠F=90°, ∠D=30°, ∠A=45°, then the sum of ∠1 and ∠2 is equal to which of the following?
(A) 270°
(B) 210°
(C) 180°
(D) 150°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, the diagonals AC and BD of rhombus ABCD intersect at point O. Line AE is drawn perpendicular to BC at point E, and line OE is connected. If OB = 6 and the area of rhombus ABCD is 54, what is the length of OE?
Choices:
(A) 4
(B) 4.5
(C) 8
(D) 9

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the quadrilateral ABCD shown in the figure, where AB is parallel to CD, angle C is 90 degrees, AB is 8 units long, and AD is equal to CD, both measuring 5 units. Points M and N are moving points on BC and AB respectively, while E and F are the midpoints of DM and MN. What is the minimum length of EF?
Choices:
(A) 3
(B) 2.5
(C) 2
(D) 1

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, PA is a tangent to circle O, with point A as the point of tangency. If ∠APO = 36°, what is the measure of ∠AOP?
(A) 54°
(B) 64°
(C) 44°
(D) 36°

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the rhombus ABCD, E is the midpoint of AB. If EF is parallel to BC and intersects AC at point F, and EF = 4, what is the length of CD?
(A) 2
(B) 4
(C) 6
(D) 8

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of x.
Options:
(A) 5.5
(B) 5.5 √2
(C) 11
(D) 11 √2

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, quadrilateral ABCD is inscribed in circle O. If ∠B = 130°, what is the measure of ∠AOC?
Choices:
(A) 130°
(B) 120°
(C) 110°
(D) 100°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In rhombus LMPQ, if the measure of angle QLM is 2x^2 - 10, the measure of angle QPM is 8x, and MP is 10, what is the measure of angle LQM?
Choices:
(A) 10
(B) 20
(C) 70
(D) 80

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, point P is a fixed point outside line l, point A is a point on line l, and the symmetric point of point P about line l is denoted as P1. If line l is rotated clockwise 30° around point A to form line l', where point P2 is symmetric to point P about line l', what is the measure of angle P1AP2?
Choices:
(A) 30°
(B) 45°
(C) 60°
(D) 75°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the measure of angle D.
Choices:
(A) 36
(B) 74
(C) 78
(D) 128

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, points A, B, C, and D are all on circle O. If ∠COD = 80°, what is the sum of ∠ABD and ∠OCA?
Choices:
(A) 45°
(B) 50°
(C) 55°
(D) 60°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In a practical activity class, Xiao Ming measured the distance between points B and C in a pond. He selected point A on one side of the pond and then measured the midpoints D and E of AB and AC, with DE equal to 10m. Based on this, what is the distance between points B and C in the pond?
Choices:
(A) 5m
(B) 10m
(C) 15m
(D) 20m

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the parallelogram ABCD shown, where AB=6, AD=9, the angle bisector of ∠BAD intersects BC at point E and extends to point F on the extension of DC, with EF=2. What is the perimeter of triangle CEF?
Choices:
(A) 8
(B) 9.5
(C) 10
(D) 11.5

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, AD is parallel to BC, ∠D = ∠ABC, point E is a point on the side DC, connecting AE intersects the extension of BC at point H, point F is a point on side AB such that ∠FBE = ∠FEB, the angle bisector of ∠FEH, EG intersects BH at point G. If ∠DEH = 98°, what is the degree measure of ∠BEG?
Choices:
(A) 39°
(B) 40°
(C) 41°
(D) 42°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the measure of angle PNM.
Choices:
(A) 36
(B) 44
(C) 63
(D) 88

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, in quadrilateral ABCD, AB = 10, AD = 6, EC is perpendicular to AE, FC is perpendicular to AB, and CF = 3. What is the length of CE?
Choices:
(A) 5
(B) 6
(C) 8
(D) 10

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, if the side length of rhombus ABCD is 6 and ∠ABC = 60°, what is the length of diagonal AC?
Choices:
(A) 3
(B) 3√{3}
(C) 6
(D) 6√{3}

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If triangle △ABC is rotated clockwise 35° around point C to form △A'B'C, where A'B' intersects AC at point D and ∠ADC = 90°, what is the measure of ∠A in degrees?
(A) 35°
(B) 65°
(C) 55°
(D) 25°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Calculate the area of the parallelogram and round to the nearest tenth if needed.
Options:
(A) 35
(B) 38.4
(C) 70
(D) 140

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the quadrilateral ABCD shown in the figure, where AB and CD are not parallel, M and N are the midpoints of AD and BC respectively. If AB = 4 and DC = 2, which of the following cannot be the length of MN?
Choices:
(A) 3
(B) 2.5
(C) 2
(D) 1.5

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Calculate the perimeter of triangle ABC.
Choices:
(A) 20
(B) 24
(C) 30
(D) 32

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In triangle KLM, JH is a midsegment. Determine the value of x.
Choices:
(A) 5
(B) 10
(C) 11
(D) 22

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In rhombus XYZW, if angle WYZ measures 53 degrees, WV is 3 units, XV is 2a - 2, and ZV is (5a + 1) / 4, what is the length of XZ?
Choices:
(A) 2
(B) 4
(C) 8
(D) 16

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Given that Q R is parallel to T S, Q T is parallel to R S, and the measure of angle 1 is 131 degrees, what is the measure of angle 5 in the figure?
(A) 49
(B) 59
(C) 69
(D) 79

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, given line segment AB, a perpendicular line is drawn from point B on AB, and a point C is taken on the perpendicular line such that BC = 1/2 AB; line AC is drawn, with point C as the center, an arc is drawn with CB as the radius intersecting AC at point D; then, with point A as the center, an arc is drawn with AD as the radius intersecting AB at point P, what is the value of AP/AB?
Choices:
(A) (√5-1)/2
(B) (√5+1)/2
(C) (3-√5)/2
(D) √2/2

Answer: $\boxed{A}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, two circles with center O are drawn, where the chord AB of the larger circle is tangent to the smaller circle. Given that AB = 10cm, what is the area of the ring formed by the two circles?
Choices:
(A) 5πcm²
(B) 25πcm²
(C) 50πcm²
(D) 100πcm²

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, lines l1, l2, and l3 are parallel and intersect at points A, B, and C. Line DF intersects l1, l2, and l3 at points D, E, and F respectively. Line AC intersects DF at point H. If AB = 5, BH = 1, CH = 2, what is the value of EF/DE?
Choices:
(A) 1/5
(B) 1/3
(C) 2/5
(D) 3/5

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, AB and AC are chords of circle O, with OE perpendicular to AB and OF perpendicular to AC, and E and F as the respective feet of the perpendiculars. If EF = 3.5, what is the length of BC?
(A) 3.5
(B) 7
(C) 10.5
(D) 9

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the diagram, in regular octagon ABCDEFGH, what is the measure of angle EAG?
Choices:
(A) 30°
(B) 40°
(C) 45°
(D) 50°

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the parallelogram ABCD, where AD = 8, AB = 3, AE bisects angle BAD and intersects BC at point E, what is the length of CE?
Choices:
(A) 2
(B) 3
(C) 4
(D) 5

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the figure, the base radius of a conical chimney cap is 15cm, and the slant height is 20cm. What is the minimum amount of sheet metal required to make such a chimney cap?
Choices:
(A) 150πcm^{2}
(B) 300πcm^{2}
(C) 450πcm^{2}
(D) 600πcm^{2}

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If the measure of angle DGF is 53 degrees and the measure of angle AGC is 40 degrees, what is the measure of angle 2?
Choices:
(A) 40
(B) 43
(C) 50
(D) 53

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Find the length of segment QR in parallelogram NQRM.
Choices:
(A) 13
(B) 14
(C) 15
(D) 16

Answer: $\boxed{C}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the perimeter of triangle DEF if triangle ABC is similar to triangle DEF, with AB = 5, BC = 6, AC = 7, and DE = 3.
Choices:
(A) 9.2
(B) 10.8
(C) 18
(D) 31.7

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, if ∠1 is equal to ∠2, and ∠D is 78°, what is the measure of ∠BCD?
(A) 98°
(B) 62°
(C) 88°
(D) 102°

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

If two equal circles with the maximum possible diameter are cut out of a rectangle of card with dimensions 16 by 8, what is the approximate area of the remaining paper after the circles have been cut out?
(A) 104
(B) 78
(C) 54
(D) 27
(E) 13

Answer: $\boxed{D}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, two right-angled triangles are positioned such that their hypotenuses are parallel to each other, and the right angles of each triangle are on the hypotenuse of the other triangle. What is the measure of angle ∠1?
Choices:
(A) 90°
(B) 75°
(C) 65°
(D) 60°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the given diagram, points A, B, C, D lie on circle O, with OB perpendicular to AC. If ∠BOC is 56°, what is the measure of ∠ADB?
Choices:
(A) 26°
(B) 28°
(C) 34°
(D) 56°

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In the right triangle ABC, where angle ACB is 90 degrees, three squares are constructed outside triangle ABC using its sides as edges. Let S1, S2, and S3 represent the areas of these three squares. If S1 is 3 and S2 is 10, what is the value of S3?
(A) 5
(B) 7
(C) 13
(D) 15

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

Determine the value of x.
Options:
(A) 11.4
(B) 22.6
(C) 32.3
(D) 43.2

Answer: $\boxed{B}$


You are a helpful assistant good at solving math problems with step-by-step reasoning. You should first thinks about the reasoning process in the mind and then provides the user with the answer. Your answer must be in latex format and wrapped in $...$.The reasoning process and answer are enclosed within <think> </think> and <answer> </answer> tags, respectively, i.e., <think> Since $1+1=2$, so the answer is $2$. </think><answer> $2$ </answer>, which means your output should start with <think> and end with </answer>.

In right triangle ABC, angle C is 90 degrees. Arcs are drawn with vertex A as the center and appropriate lengths as radii, intersecting AC and AB at points M and N. Then, arcs are drawn with points M and N as centers, with lengths greater than 0.5 times MN as radii. These two arcs intersect at point P, and ray AP intersects side BC at point D. If CD = 4 and AB = 15, point E is a moving point on segment AB. When DE is at its shortest, what is the area of triangle AED?
Choices:
(A) 15
(B) 30
(C) 45
(D) 60

Answer: $\boxed{B}$