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>.

P is the incenter of \angle X Y Z. Find m \angle L Z P.
Choices:
(A) 20
(B) 27
(C) 31
(D) 32

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>.

如图,已知直线AB∥CD,∠BEG的平分线EF交CD于点F,若∠1=42°,则∠2等于()
Choices:
(A) 159°
(B) 148°
(C) 142°
(D) 138°

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>.

如图所示,在等边三角形ABC中,AD⊥BC,E为AD上一点,∠CED=50°,则∠ABE等于()
Choices:
(A) 10°
(B) 15°
(C) 20°
(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>.

Find the area of the shaded sector. Round to the nearest tenth, if necessary.
Choices:
(A) 10.8
(B) 59.6
(C) 60.2
(D) 333.9

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>.

Find m \widehat B X.
Choices:
(A) 21
(B) 45
(C) 63
(D) 117

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>.

如图,DE、FG分别是△ABC的AB、AC边上的垂直平分线,且∠BAC=100°,那么∠DAF的度数为()
Choices:
(A) 10°
(B) 20°
(C) 30°
(D) 40°

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 accompanying diagram, ABC is an equilateral triangle with a perimeter of 30. What is the length of altitude h of this triangle?
Choices:
(A) 5\sqrt(2)
(B) 5\sqrt(3)
(C) 10\sqrt(2)
(D) 10\sqrt(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>.

如图,在△ABC中,点D、E分别是边AB、AC上的点,DE垂直平分AB,∠C=90°,∠BAC=15°．若BC=3cm,则AE的长度为()
Choices:
(A) 9cm
(B) 6cm
(C) 5cm
(D) 4cm

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>.

如图,P是圆O外的一点,PA、PB与圆O分别相切于点A、B,C是劣弧⁀{AB}上任一点,过点C的切线分别交PA、PB于点D、E．若∠P=38°,则∠DOE=()
Choices:
(A) 38°
(B) 52°
(C) 70°
(D) 71°

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>.

如图,AD是⊙O的切线,切点为A,AC是⊙O的直径,CD交⊙O于点B,连接OB,若⁀{AB}的度数为70°,则∠D的大小为()
Choices:
(A) 70°
(B) 60°
(C) 55°
(D) 35°

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 x so that the quadrilateral is a parallelogram.
Choices:
(A) 28
(B) 30
(C) 90
(D) 112

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>.

Find F B if S A and F B are altitudes and \triangle R S T \sim \triangle E F G.
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>.

For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure.
Choices:
(A) \frac { 3 } { 4 }
(B) \frac { \sqrt { 3 } } { 2 }
(C) \frac { 2 } { \sqrt { 3 } }
(D) \frac { 4 } { 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>.

如图所示．△ABC内接于⊙O,若∠OAB=28°,则∠C的大小是()
Choices:
(A) 56°
(B) 62°
(C) 28°
(D) 32°

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>.

如图,已知△ABC的面积为12,点D在线段AC上,点F在线段BC的延长线上,且BC=4CF,四边形DCFE是平行四边形,则图中阴影部分的面积为()
Choices:
(A) 2
(B) 3
(C) 4
(D) 6

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>.

如图,AB是⊙O的直径,弦CD丄AB,∠CAB=20°,则∠BOD等于()
Choices:
(A) 30°
(B) 40°
(C) 45°
(D) 50°

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>.

如图,在正方形ABCD中,G为CD的中点,连结AG并延长,交BC边的延长线于点E,对角线BD交AG于点F,已知AF=2,则线段AE的长是()
Choices:
(A) 4
(B) 6
(C) 8
(D) 10

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>.

如图,PA,PB分别与⊙O相切于A,B点,C为⊙O上一点,∠P=66°,则∠C=()
Choices:
(A) 57°
(B) 60°
(C) 63°
(D) 66°

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>.

Find y.
Choices:
(A) 3 \sqrt { 42 }
(B) 6 \sqrt { 42 }
(C) 48
(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>.

如图,AB为⊙O的直径,CD为弦,AB⊥CD,如果∠BOC=70°,则∠ABD的度数为()
Choices:
(A) 35°
(B) 45°
(C) 55°
(D) 70°

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>.

如图,AB、CD是⊙O的两条直径,且AB⊥CD,⁀{CE}=\frac{1}{2}⁀{EB},P为直径CD上一动点,若⊙O的直径AB=2,则△PEB周长的最小值是()
Choices:
(A) 3
(B) 4
(C) 2√{3}
(D) √{3}+1

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>.

如图,△ADB与△AEC相似,AB=3,DB=2,EC=6,则BC等于()
Choices:
(A) 9
(B) 6
(C) 5
(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>.

如图所示，在△ABC中，已知点D，E，F分别为边BC，AD，CE的中点，且S△ABC＝4cm2，则S△DEF等于（）
Choices:
(A) 2cm2
(B) 1cm2
(C) 0.5cm2
(D) 0.25cm2

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>.

如图,四边形ABCD为⊙O的内接四边形．弦AB与DC的延长线相交于点G,AO⊥CD,垂足为E,连接BD,∠GBC=48°,则∠DBC的度数为()
Choices:
(A) 84°
(B) 72°
(C) 66°
(D) 48°

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>.

如图,在⊙O中,OC⊥直径AB,P为BA延长线上一点,PC交⊙O于点Q,若∠P=28°,则∠B=()
Choices:
(A) 10°
(B) 14°
(C) 17°
(D) 27°

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>.

如图,⊙O是△ABC的外接圆,∠ACO=45°,则∠B的度数为()
Choices:
(A) 30°
(B) 35°
(C) 40°
(D) 45°

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>.

如图,在⊙O的内接△ABC中,∠ABC=30°,AC的延长线与过点B的⊙O的切线相交于点D,若⊙O的半径OC=2,BD∥OC,则CD的长为()
Choices:
(A) 1+\frac{√{3}}{3}
(B) \frac{4√{3}}{3}
(C) \frac{2√{3}}{3}
(D) 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>.

如图在△ABC中，已知点D、E、F分别为边BC，AB，AC的中点，且△ABC的面积是12，则阴影部分的面积是（）
Choices:
(A) 2
(B) 4
(C) 6
(D) 8

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>.

如图△ABC中,∠A=36°,AB=AC,BF平分∠ABC,E是AF的中点,DE⊥AC交AB于D,连接DC交BF于P,∠DPB的度数是()
Choices:
(A) 36°
(B) 54°
(C) 72°
(D) 90°

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>.

Find x. Assume that segments that appear to be tangent are tangent.
Choices:
(A) 15
(B) 21
(C) 36
(D) 72

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>.

边长为10cm的正方形ABCD绕对角线的交点O旋转到得到正方形OA′B′C′,如图所示,则阴影部分面积为()
Choices:
(A) 100cm²
(B) 75cm²
(C) 50cm²
(D) 25cm²

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>.

AB and DE are parallel. The measure of angle BAC is 30 , and the measure of angle CDE is 50. What is the measure of angle ACD?
Choices:
(A) 100
(B) 90
(C) 80
(D) 70
(E) cannot be determined from the information

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>.

如图,点A,B,C在⊙O上,若∠ACB=112°,则∠α=()
Choices:
(A) 68°
(B) 112°
(C) 136°
(D) 134°

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>.

如图,△ABC为⊙O的内接三角形,若∠ADC=115°,则∠AOC的度数是()
Choices:
(A) 115°
(B) 130°
(C) 150°
(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>.

如图所示,圆锥的母线长为10cm,其侧面展开图是圆心角为216°的扇形,则该圆锥的高为()
Choices:
(A) 5cm
(B) 6cm
(C) 7cm
(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>.

Use the Pythagorean Theorem to find the length of the hypotenuse of the right triangle.
Choices:
(A) 3
(B) 4
(C) 5
(D) \sqrt { 34 }

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>.

Find the length of F G.
Choices:
(A) 17
(B) 35
(C) 39
(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>.

Find x in the figure.
Choices:
(A) 14
(B) 31
(C) 45
(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>.

Find Q S.
Choices:
(A) 3
(B) 4
(C) 6
(D) 9

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>.

如图,在⊙O中,弦AB、DC的延长线相交于点P．如果∠AOD=110°,∠BDC=20°,那么∠P=()
Choices:
(A) 45°
(B) 55°
(C) 60°
(D) 35°

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>.

如图,BD是⊙O的直径,点A在BD的延长线上,AC切⊙O于点C,∠A=30°,则∠B=()
Choices:
(A) 60°
(B) 30°
(C) 15°
(D) 45°

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 Q R S T is a parallelogram, find x.
Choices:
(A) 5.4
(B) 9
(C) 11
(D) 13

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>.

如图所示,△ABC中,DE∥BC,AD=5,AB=10,DE=6,则BC的值为()
Choices:
(A) 6
(B) 12
(C) 18
(D) 24

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>.

如图,图①是一个四边形纸条ABCD,其中AB∥CD,E,F分别为边AB,CD上的两个点,将纸条ABCD沿EF折叠得到图②,再将图②沿DF折叠得到图③,若在图③中,∠FEM=26°,则∠EFC的度数为()
Choices:
(A) 52°
(B) 64°
(C) 102°
(D) 128°

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, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 10.
Choices:
(A) 55
(B) 70
(C) 110
(D) 125

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>.

Polygon B C D E \cong polygon R S T U. Find z.
Choices:
(A) 3
(B) 10
(C) 20
(D) 42

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>.

如图,在△ABC中,AD是角平分线,AE是中线,CF⊥AD于点F,AC=5,AB=13,则EF的长为()
Choices:
(A) \frac{13}{5}
(B) \frac{13}{4}
(C) 3
(D) 4

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>.

如图,△ABC顶点A、B、C都在⊙O上,连接AO、BO,若∠OAB=50°,则∠ACB的大小是()
Choices:
(A) 25°
(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>.

Find x.
Choices:
(A) 42
(B) 56
(C) 70
(D) 84

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>.

如图,把直角三角板的直角顶点O放在破损玻璃镜的圆周上,两直角边与圆弧分别交于点M、N,量得OM=8cm,ON=6cm,则该圆玻璃镜的半径是()
Choices:
(A) √{10}cm
(B) 5cm
(C) 6cm
(D) 10cm

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>.

如图,四边形OABC为菱形,点A、B在以点O为圆心的弧DE上,若AO=3,∠1=∠2,则扇形ODE的面积为()
Choices:
(A) \frac{3}{2}π
(B) 2π
(C) \frac{5}{2}π
(D) 3π

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>.

如图,DE是△ABC中边AC的垂直平分线,若BC=18cm,AB=10cm,则△ABD的周长为()
Choices:
(A) 16cm
(B) 18cm
(C) 26cm
(D) 28cm

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>.

如图，在△ABC中，点D、E分别是BC、AC的中点，BF平分∠ABC，交DE于点F，若BC＝6，则DF的长是（）
Choices:
(A) 2
(B) 3
(C) 6
(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>.

如图,A、B、C三点在圆O上,AD平分∠BAC,∠DAC=35°,则∠BOC=()
Choices:
(A) 35°
(B) 70°
(C) 120°
(D) 140°

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>.

如图,A,B,C为⊙O上三点,若∠ACB=20°,则∠BAO的大小为()
Choices:
(A) 40°
(B) 60°
(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>.

如图,ABCD为圆内接四边形,若∠A=60°,则∠C等于()
Choices:
(A) 30°
(B) 60°
(C) 120°
(D) 300°

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>.

如图,边长12的正方形ABCD中,有一个小正方形EFGH,其中E、F、G分别在AB、BC、FD上．若BF=3,则小正方形的边长为多长？()
Choices:
(A) 2√{3}
(B) 3.75
(C) 5
(D) 6

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 x = 7 \sqrt { 3 }, find b.
Choices:
(A) 7
(B) 7 \sqrt { 3 }
(C) 14 \sqrt { 3 }
(D) 42

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>.

如图,△ABC与△ADE是位似图形,且相似比为2:3,若△ABC的面积为18,则△ADE的面积为()
Choices:
(A) 6
(B) 8
(C) 9
(D) 12

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>.

Find C P.
Choices:
(A) 4
(B) 8
(C) 10
(D) 12

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>.

如图,在▱ABCD中,AB=18,AD=12,∠ABC的平分线交CD于点F,交AD的延长线于点E,CG⊥BE,垂足为G,若EF=4,则线段CG的长为()
Choices:
(A) 2√{35}
(B) 6√{3}
(C) 4√{10}
(D) 8√{2}

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>.

Find C D if A B = 6, A F = 8, B C = x, C D = y, D E = 2 y - 3, and F E = x + \frac { 10 } { 3 }.
Choices:
(A) 9
(B) 10
(C) 12
(D) 15

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>.

如图，AC为矩形ABCD的对角线，∠BAC的平分线交BC于点E，BM⊥AE于点M，交AC于点F．若点N是BC的中点，连接MN．已知AB＝6，BC＝8．则MN的长为（）
Choices:
(A) 3.5
(B) 3
(C) 2.5
(D) 2

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>.

如图,在△ABC中,DE∥BC,DE分别与AB、AC相交于点D、E,若EC=2,AC=8,则DE:BC的值为()
Choices:
(A) \frac{2}{3}
(B) \frac{1}{2}
(C) \frac{3}{4}
(D) \frac{1}{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 \odot R, S U = 20, Y W = 20, and m \widehat Y X = 45. Find m \widehat S U.
Choices:
(A) 20
(B) 30
(C) 45
(D) 90

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>.

Find A B.
Choices:
(A) 1.6
(B) 2.8
(C) 3.6
(D) 4

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, m \angle 8 = 96 and m \angle 12 = 42. Find the measure of \angle 9.
Choices:
(A) 42
(B) 84
(C) 94
(D) 96

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>.

如图，已知圆锥的底面圆的直径BC＝6，高OA＝4，则这个圆锥的侧面展开图的面积为（）
Choices:
(A) 30π
(B) 12×√{3}×π
(C) 15π
(D) 22.5×π

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>.

如图,点A、B、C都在⊙O上,点B为弧AC的中点,若∠AOB=72°,则∠OAC的度数是()
Choices:
(A) 18°
(B) 30°
(C) 36°
(D) 72°

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>.

如图,AB∥CD,∠AGE=128°,HM平分∠EHD,则∠MHD的度数是()
Choices:
(A) 46°
(B) 23°
(C) 26°
(D) 24

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>.

The diagram at the right shows the construction of a perpendicular, line PX, to a line l from point P. The arc drawn from point P intersects line l at A and B, and the arcs drawn from points A and B intersect line PX at C.  Which of the statements is not always true about this construction?
Choices:
(A) PA = PB
(B) AX = BX
(C) PX = CX
(D) AC = BC

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>.

如图，四边形ABCD内接于⊙O，DA＝DC，若∠CBE＝45°，则∠DAC的度数为（）
Choices:
(A) 70°
(B) 67.5°
(C) 62.5°
(D) 65°

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>.

如图，在⊙O中，弦AC与半径OB交于点D，连接OA，BC，若∠B＝60°，∠ADB＝116°，则∠AOB的度数为（）
Choices:
(A) 132°
(B) 120°
(C) 112°
(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>.

如图,点C是线段AB上一点,点P是AC的中点,点Q是BC的中点,已知线段AC=8cm,线段BC=4cm,则线段PQ为()
Choices:
(A) 2cm
(B) 4cm
(C) 6cm
(D) 12cm

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>.

Polygon A B C D \sim polygon A E F G, m \angle A G F = 108, G F = 14, A D = 12, D G = 4.5, E F = 8, and A B = 26. Find the perimeter of trapezoid A B C D.
Choices:
(A) 12
(B) 52
(C) 73.2
(D) 100

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>.

如图,⊙O直径AB=8,∠CBD=30°,则CD=()
Choices:
(A) 4
(B) 6
(C) 3
(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>.

Find the perimeter of the triangle.
Choices:
(A) 40.5
(B) 60.2
(C) 71.7
(D) 75.7

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>.

如图,在直线l上顺次取A、B、C三点,使得AB=5cm,BC=3cm,如果O是线段AC的中点,那么线段OB长为()
Choices:
(A) 1cm
(B) 1.5cm
(C) 2cm
(D) 4cm

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>.

如图,A、B、C、D为⊙O上四点,AB、DC交于E点,AD、BC交于点F．若∠E=36°,∠F=30°,则∠A的度数为()
Choices:
(A) 30°
(B) 40°
(C) 57°
(D) 70°

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>.

如图,已知△ACD∽△BCA,若CD=4,AC=6,则BC等于()
Choices:
(A) 9
(B) 10
(C) 11
(D) 12

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>.

如图,在菱形ABCD中,AC、BD为对角线,AC=6,BD=8,则阴影部分的面积为()
Choices:
(A) 48
(B) 10
(C) 12
(D) 24

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>.

如图,已知直线a∥b,直线c与a、b分别交于A、B；且∠1=120°,则∠2=()
Choices:
(A) 60°
(B) 120°
(C) 30°
(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>.

Points S, T, and U are the midpoints of D E, E F, and D F, respectively. Find x.
Choices:
(A) 4
(B) 4.5
(C) 5
(D) 5.5

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>.

如图,⊙O是△ABC的外接圆,CD是直径,∠B=50°,则∠ACD的度数是()
Choices:
(A) 30°
(B) 40°
(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 quadrilateral A B C D, A C = 188, B D = 214, m \angle B P C = 70, and P is the midpoint of A C and B D. Find the perimeter of quadrilateral A B C D.
Choices:
(A) 343.1
(B) 423.1
(C) 561.2
(D) 671.2

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>.

如图,在▱ABCD中,用直尺和圆规作∠BAD的平分线AG交BC于点E．若BF=6,AB=5,则AE的长为()
Choices:
(A) 4
(B) 6
(C) 8
(D) 10

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>.

如图,Rt△ABC中,∠C=90°,AB的垂直平分线DE交AC于点E,连接BE,若∠A=35°,则∠CBE的度数是()
Choices:
(A) 15°
(B) 20°
(C) 30°
(D) 45°

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>.

如图，矩形ABCD的对角线AC，BD交于点O，AB＝6，BC＝8，过点O作OM⊥AC，交BC于点M，过点M作MN⊥BD，垂足为N，则OM+MN的值为（）
Choices:
(A) 4.8
(B) 3.2
(C) 2.4
(D) 1.2

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>.

Use parallelogram A B C D to find B C.
Choices:
(A) 6
(B) 9
(C) 12
(D) 18

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 m \widehat F E = 118, m \widehat A B = 108, m \angle E G B = 52, and m \angle E F B = 30. Find m \widehat A C.
Choices:
(A) 30
(B) 52
(C) 108
(D) 118

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>.

如图,已知E是正方形ABCD的边AD的延长线上一点,BE交AD于点F,若CD=6,FD=2,则ED的长是()
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 \odot P, P D = 10, P Q = 10, and Q E = 20, find P E.
Choices:
(A) 10
(B) 20
(C) 10 \sqrt { 5 }
(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>.

如图所示，在△ABC中，已知点D，E，F分别为边BC，AD，CE的中点，且S△ABC＝4cm2，则S△DEF等于（）
Choices:
(A) 2cm2
(B) 1cm2
(C) 0.5cm2
(D) 0.25cm2

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>.

如图,小明从A点出发,沿直线前进10米后向左转36°,再沿直线前进10米,再向左转36°……照这样走下去,他第一次回到出发点A点时,一共走的路程是()
Choices:
(A) 100米
(B) 110米
(C) 120米
(D) 200米

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>.

The diagram at the right shows the construction of the perpendicular bisector of AB. Which statement is not true?
Choices:
(A) AC = CB
(B) AC = 2AB
(C) CB = 1/2*AB
(D) AC + CB = AB

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>.

如图,圆内接四边形ABCD的边AB过圆心O,过点C的切线与边AD所在直线垂直于点M,若∠ABC=55°,则∠ACD等于()
Choices:
(A) 20°
(B) 35°
(C) 40°
(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>.

Use parallelogram to find z.
Choices:
(A) 2
(B) 7
(C) 11
(D) 13

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>.

如图,在⊙O中,弦BC∥半径OA,AC与OB相交于M,∠C=20°,则∠AMB的度数为()
Choices:
(A) 30°
(B) 60°
(C) 50°
(D) 40°

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>.

如图,⊙O是△ABC的外接圆,∠C=35°,则∠OBA的度数为()
Choices:
(A) 50°
(B) 60°
(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>.

如图，在△ABC中，点D在边BC上，点E，F分别是AD，CE的中点，且△BEF的面积为3，则△ABC的面积是（）
Choices:
(A) 9
(B) 10
(C) 11
(D) 12

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, \triangle A B C is isosceles, \triangle D C E is equilateral, and \triangle F C G is isosceles. Find the measure of the \angle 4 at vertex C.
Choices:
(A) 15
(B) 16
(C) 17
(D) 18

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>.

如图,A、B、C在⊙O上,∠OAB=22.5°,则∠ACB的度数是()
Choices:
(A) 11.5°
(B) 112.5°
(C) 122.5°
(D) 135°

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>.

如图,长方体的长为5,宽为3,高为12,点B离点C的距离为2,一只蚂蚁如果要沿着长方体的表面从点A爬到点B,需要爬行的最短距离是()
Choices:
(A) √{119}
(B) 13
(C) √{5}+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>.

如图,在⊙O中∠O=50°,则∠A的度数为()
Choices:
(A) 50°
(B) 20°
(C) 30°
(D) 25°

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>.

Find the area of the regular polygon. Round to the nearest tenth.
Choices:
(A) 73.0
(B) 292.1
(C) 584.2
(D) 1168.5

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>.

如图,AB、AC是⊙O的两条弦,∠A=25°,过点C的切线与OB的延长线交于点D,则∠D的度数()
Choices:
(A) 25°
(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>.

如图,OA,OB分别为⊙O的半径,若CD⊥OA,CE⊥OB,垂足分别为D,E,∠P=70°,则∠DCE的度数为()
Choices:
(A) 70°
(B) 60°
(C) 50°
(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>.

Find y in the figure.
Choices:
(A) 12
(B) 26.3
(C) 28
(D) 168

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>.

如图，在平面直角坐标系xOy中，四边形ABCD是菱形，∠ABC＝120°，点B的坐标为（0，﹣2），则菱形ABCD的面积为（）
Choices:
(A) 16
(B) 32
(C) 8√{3}
(D) 16√{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>.

如图,用半径为10,圆心角为144°的扇形纸片围成一个圆锥(接缝处忽略不计),则该圆锥的底面半径是()
Choices:
(A) 3
(B) 4
(C) 5
(D) 6

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>.

如图，平行四边形ABCD的对角线AC与BD相交于点O，AB⊥AC，若AB＝8，BD＝20，则AC的长是（）
Choices:
(A) 6
(B) 10
(C) 12
(D) 18

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>.

如图，AB＝AC，AD＝AE，∠BAC＝∠DAE，∠1＝25°，∠2＝30°，连接BE，点D恰好在BE上，则∠3＝（）
Choices:
(A) 60°
(B) 55°
(C) 50°
(D) 0°

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>.

如图,BC是⊙O的直径,AD⊥BC,若∠D=36°,则∠BAD的度数是()
Choices:
(A) 72°
(B) 54°
(C) 45°
(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>.

Find x so that m \parallel n.
Choices:
(A) 13
(B) 14
(C) 15
(D) 16

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>.

如图,已知⊙O是△ABC的外接圆,连接AO,若∠B=40°,则∠OAC=()
Choices:
(A) 40°
(B) 50°
(C) 60°
(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>.

Find B C if B E = 24, C D = 32, and A B = 33.
Choices:
(A) 11
(B) 12
(C) 16
(D) 44

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>.

如下图,在平行四边形ABCD中,AE平分∠BAD交DC边于点E,DF⊥AE于F,已知∠ADF=50°,∠C的度数为()
Choices:
(A) 85°
(B) 80°
(C) 75°
(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>.

如图,△ABC中,AE交BC于点D,∠C=∠CBE,AD:DE=3:5,BD=4,则DC的长等于()
Choices:
(A) \frac{15}{4}
(B) \frac{12}{5}
(C) \frac{20}{3}
(D) \frac{17}{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>.

如图，C，D是⊙O上直径AB两侧的两点，设∠ABC＝35°，则∠BDC＝（）
Choices:
(A) 85°
(B) 75°
(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>.

如图,BC=\frac{1}{2}AB,D为AC的中点,DC=3cm,则AB的长是()
Choices:
(A) 4cm
(B) \frac{9}{2}cm
(C) 5cm
(D) \frac{11}{2}cm

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>.

如图，AB为⊙O的直径，∠BED＝20°，则∠ACD的度数为（）
Choices:
(A) 80°
(B) 75°
(C) 70°
(D) 65°

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>.

如图,在Rt△ABC中,∠ACB=90°,∠B=34°,以BC为直径的⊙O交AB于点D,E是⊙O上一点,且=,连接OE,过点E作EF⊥OE,交AC的延长线于点F,则∠F的度数为()
Choices:
(A) 92°
(B) 108°
(C) 112°
(D) 124°

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>.

如图,C、D是以线段AB为直径的⊙O上两点(位于AB两侧),CD=AD,且∠ABC=70°,则∠BAD的度数是()
Choices:
(A) 50°
(B) 45°
(C) 35°
(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>.

Use parallelogram M N P R to find m \angle N R P.
Choices:
(A) 33
(B) 38
(C) 71
(D) 109

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>.

如图,铁道口的栏杆短臂OA长1m,长臂OB长8m,当短臂外端A下降0.5m时,长臂外端B升高()
Choices:
(A) 2m
(B) 4m
(C) 4.5m
(D) 8m

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>.

如图,在⊙O中,弦AC∥半径OB,∠BOC=40°,则∠OAB的度数为()
Choices:
(A) 25°
(B) 20°
(C) 60°
(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>.

如图,⊙O的直径AB=6,点C为⊙O外一点,CA、CB分别交⊙O于E、F,cos∠C=\frac{2}{3},则EF的长为()
Choices:
(A) 3
(B) 2
(C) 1.5
(D) 4

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>.

如图,DE∥BC,分别交△ABC的边AB、AC于点D、E,\frac{AD}{AB}=\frac{1}{3},若AE=1,则EC=()
Choices:
(A) 2
(B) 3
(C) 4
(D) 6

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>.

如图,圆O的直径AB为4,点C在圆O上,∠ACB的平分线交圆O于点D,连接AD、BD,则AD的长等于()
Choices:
(A) 2
(B) 3
(C) 2√{2}
(D) 2√{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>.

如图,将三角形纸板的直角顶点放在直尺的一边上,∠1=20°,∠2=40°,则∠3等于()
Choices:
(A) 50°
(B) 30°
(C) 20°
(D) 15°

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>.

如图,直线m∥n,将含有45°角的三角板ABC的一个锐角顶点C放在直线n上,则∠1+∠2等于()
Choices:
(A) 30°
(B) 45°
(C) 60°
(D) 90°

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>.

如图,小丽自己动手做了一顶圆锥形的彩纸圣诞帽,母线长是30cm,底面半径是10cm,她至少需要彩纸()
Choices:
(A) 200πcm^{2}
(B) 300πcm^{2}
(C) 400πcm^{2}
(D) 30cm^{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>.

如图，四边形ABCD为⊙O的内接四边形，已知∠BOD＝140°，则∠BCD的度数为（）
Choices:
(A) 100°
(B) 110°
(C) 120°
(D) 140°

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>.

如图,⁀{BC}=⁀{CD}=⁀{DE},已知AB是⊙O的直径,∠BOC=40°,那么∠AOE=()
Choices:
(A) 40°
(B) 60°
(C) 80°
(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>.

如图,AD∥BE∥CF,直线l1,l2与这三条平行线分别交于点A,B,C和点D,E,F,\frac{AB}{BC}=\frac{2}{3},DE=4,则EF的长为()
Choices:
(A) \frac{8}{3}
(B) \frac{20}{3}
(C) 6
(D) 10

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>.

如图,四边形ABCD中,∠B=∠D,⊙O经过点A,C,D,与BC相交于点E,连AC,AE,若∠D=72°,则∠BAE为()
Choices:
(A) 28°
(B) 36°
(C) 40°
(D) 48°

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>.

一只因损坏而倾斜的椅子,从背后看到的形状如图所示,其中两组对边的平行关系没有发生变化．若∠1=76°,则∠2的度数是()
Choices:
(A) 76°
(B) 86°
(C) 104°
(D) 114°

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>.

已知:如图,在⊙O的内接四边形ABCD中,AB是直径,∠BCD=130°,过D点的切线PD与直线AB交于P点,则∠ADP的度数为()
Choices:
(A) 40°
(B) 45°
(C) 50°
(D) 65°

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>.

Find m \widehat Y C.
Choices:
(A) 21
(B) 60
(C) 75
(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>.

如图,AB∥CE,BF交CE于点D,DE=DF,∠B=40°,则∠E的度数为()
Choices:
(A) 20°
(B) 30°
(C) 40°
(D) 15°

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>.

Find x in the parallelogram.
Choices:
(A) 7
(B) 14
(C) 15
(D) 23

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>.

Find x.
Choices:
(A) 5
(B) 7
(C) 8
(D) 10

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>.

Find m \angle 2.
Choices:
(A) 20
(B) 40
(C) 45
(D) 65

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>.

如图，在菱形ABCD中，AC与BD相交于点O，AB的垂直平分线EF交AC于点F，连接DF．若∠BAD＝80°，则∠CDF的度数为（）
Choices:
(A) 100°
(B) 80°
(C) 60°
(D) 40°

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>.

如图,在△ABC中,∠A=90°．若AB=12,AC=5,则\cosC的值为()
Choices:
(A) \frac{5}{13}
(B) \frac{12}{13}
(C) \frac{5}{12}
(D) \frac{12}{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>.

如图,A、B两处被池塘隔开,为了测量A、B两处的距离,在AB外选一点C,连接AC、BC,并分别取线段AC、BC的中点E、F,测得EF=15m,则AB的长为()
Choices:
(A) 7.5m
(B) 15m
(C) 30m
(D) 45m

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 m \angle Z.
Choices:
(A) 34
(B) 68
(C) 136
(D) 143

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>.

如图,点P为O外一点,PA为⊙O的切线,A为切点,PO交⊙O于点B．若∠P=30°,OB=3,则线段AP的长为()
Choices:
(A) 6√{6}
(B) 3√{3}
(C) 6
(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>.

如图,定点C、动点D在⊙O上,并且位于直径AB的两侧,AB=5,AC=3,过点C在作CE⊥CD交DB的延长线于点E,则线段CE长度的最大值为()
Choices:
(A) 5
(B) 8
(C) \frac{32}{5}
(D) \frac{20}{3}

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>.

如图，在△ABC中，∠ACB＝90°，AC＝6，BC＝8，则AB边上的高CD的长为（）
Choices:
(A) 4
(B) \frac{24}{5}
(C) 3√{3}
(D) 10

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>.

Find x.
Choices:
(A) 16
(B) 18
(C) 24
(D) 27

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>.

Find the area of the blue region.
Choices:
(A) 85.8
(B) 114.2
(C) 214.2
(D) 228.4

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>.

一个空间几何体的主视图和左视图都是边长为30cm的正三角形,俯视图是一个圆,那么这个几何体的侧面积是()
Choices:
(A) 250πcm²
(B) 300πcm²
(C) 450πcm²
(D) 100√πcm²

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>.

如图,AB是⊙O的直径,A,C,D在圆上,∠D=65°,则∠ABC的度数为()
Choices:
(A) 20°
(B) 25°
(C) 30°
(D) 35°

Answer: $\boxed{B}$