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{
"role": "user",
"content": "<image>As shown in the figure , the radii of the two concentric circles are N_0 and N_1 respectively , and a chord A B of the great circle is tangent to the small circle , then the length of the chord A B is ()\n\nChoices:\n3.0\n4.0\n6.0\n8.0\n\nFirst, the purpose of the proble... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the straight line a perpendicular the straight line c , the straight line b perpendicular the straight line c , if angle 1 = N_0 , then angle 2 = ()\n\nChoices:\n70.0\n90.0\n110.0\n80.0\n\nFirst, the purpose of the problem. Then, provide a descri... | |
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{
"role": "user",
"content": "<image>As shown in the figure , given the straight line a parallel b , the straight line c and a and b intersect at A and B respectively ; and angle 1 = N_0 , then angle 2 = ()\n\nChoices:\n60.0\n120.0\n30.0\n150.0\n\nFirst, the purpose of the problem. Then, provide a descripti... | |
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{
"role": "user",
"content": "<image>A flower and tree farm has an open space shaped like an isosceles trapezoid A B C D , the midpoints of each side are E , F , G , H , and the diagonal A C = N_0 is measured . Now I want to use a fence to form a quadrilateral E F G H field , then the total length of the fe... | |
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{
"role": "user",
"content": "<image>As shown in the figure , point O is on the straight line A B and O C perpendicular O D , if angle C O A = N_0 , then the size of angle D O B is ()\n\nChoices:\n36.0\n54.0\n64.0\n72.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through y... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the midpoints of each side of any quadrilateral A B C D are E , F , G , and H respectively . If the lengths of the diagonals A C and B D are all N_0 , then the perimeter of the quadrilateral E F G H is ()\n\nChoices:\n80.0\n40.0\n20.0\n10.0\n\nFi... | |
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{
"role": "user",
"content": "<image>As shown in the figure , points A , B , C are on circle O , angle A = N_0 , then the degree of angle B O C is ()\n\nChoices:\n40.0\n50.0\n80.0\n100.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Final... | |
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{
"role": "user",
"content": "<image>As shown in the figure , angle A O B = N_0 , then angle A + angle B is equal to ()\n\nChoices:\n100.0\n80.0\n50.0\n40.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Finally, write your answer in the f... | |
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{
"role": "user",
"content": "<image>As shown in the figure , triangle A B C is inscribed to circle O , A D is the diameter of circle O , angle A B C = N_0 , then the degree of angle C A D is ()\n\nChoices:\n25.0\n50.0\n65.0\n75.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, thin... | |
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{
"role": "user",
"content": "<image>Fold a paper tape with two parallel edges as shown in the figure , if angle 1 = N_0 , then angle 2 is equal to ()\n\nChoices:\n62.0\n56.0\n45.0\n30.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Final... | |
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{
"role": "user",
"content": "<image>As shown in the figure , D is the midpoint on the side of A B . Fold triangle A B C along the line passing D so that point A falls on F on B C . If angle B = N_0 , then the degree of angle E D F is ()\n\nChoices:\n50.0\n40.0\n80.0\n60.0\n\nFirst, the purpose of the probl... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , A B = A C , angle A = N_0 , B D is the height on the edge of A C , then the degree of angle D B C is ()\n\nChoices:\n18.0\n24.0\n30.0\n36.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through... | |
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{
"role": "user",
"content": "<image>As shown in the figure , given that the central angle angle B O C = N_0 , the degree of the angle of circumference angle B A C is ()\n\nChoices:\n156.0\n78.0\n39.0\n12.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning... | |
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{
"role": "user",
"content": "<image>As shown in the figure , it is known that circle O is the circumscribed circle of triangle A B D , A B is the diameter of circle O , C D is the chord of circle O , angle A B D = N_0 , then angle B C D is equal to ()\n\nChoices:\n116.0\n32.0\n58.0\n64.0\n\nFirst, the purp... | |
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{
"role": "user",
"content": "<image>As shown in the figure , it is known that E is a point on the edge B C of the diamond A B C D , and angle D A E = angle B = N_0 , then the degree of angle C D E is ()\n\nChoices:\n20.0\n25.0\n30.0\n35.0\n\nFirst, the purpose of the problem. Then, provide a description. N... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , angle A B C = N_0 , A C = N_1 , F is the intersection of height A D and B E , then the length of B F is ()\n\nChoices:\n4.0\n6.0\n8.0\n9.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through ... | |
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{
"role": "user",
"content": "<image>In the isosceles right triangle A B C , A B = A C = N_0 , point O is the midpoint of B C , and circle O intersects B C at points M and N with O as the midpoint . circle O is tangent to A B and A C , and the tangent points are respectively D , E , then the degree of angle... | |
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{
"role": "user",
"content": "<image>As shown in the figure , angle 1 = N_0 , angle C = N_1 , then the size of angle A is ()\n\nChoices:\n10.0\n20.0\n30.0\n80.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Finally, write your answer in t... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in circle O , angle A B C = N_0 , then angle A O C is equal to ()\n\nChoices:\n50.0\n80.0\n90.0\n100.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Finally, write your answer ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A , C , and B are three points on O . If angle A O C = N_0 , then the degree of angle A B C is () .\n\nChoices:\n10.0\n20.0\n40.0\n80.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in the parallelogram A B C D with circumference N_0 , A B not-equal A D , A C and B D intersect at point O , O E perpendicular B D intersects A D at E , then the perimeter of triangle A B E is ()\n\nChoices:\n4.0\n6.0\n8.0\n10.0\n\nFirst, the pur... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A B is the diameter of circle O , arc B C = arc B D , angle A = N_0 , then the degree of angle B O D is ()\n\nChoices:\n25.0\n50.0\n12.5\n30.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning s... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , angle C = N_0 , A C = N_1 cm , A B = N_2 cm , A D bisects angle B A C and intersects B C to D , D E perpendicular A B to E , then the length of E B is ()\n\nChoices:\n3.0\n4.0\n5.0\nNone\n\nFirst, the purpose of the problem. T... | |
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{
"role": "user",
"content": "<image>As shown in the figure , circle O is the circumscribed circle of triangle A B C , and it is known that angle A B O = N_0 , then the size of angle A C B is ()\n\nChoices:\n30.0\n45.0\n50.0\n60.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, thin... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A B parallel C D , A D equally divide angle B A C , if angle B A D = N_0 , then the degree of angle A C D is ()\n\nChoices:\n40.0\n35.0\n50.0\n45.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reason... | |
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{
"role": "user",
"content": "<image>As shown in the figure , triangle O A D congruent triangle O B C , and angle O = N_0 , angle C = N_1 , then angle O A D = ()\n\nChoices:\n95.0\n85.0\n75.0\n65.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , a parallel b , angle 1 = N_0 , then the degree of angle 2 is equal to ()\n\nChoices:\n50.0\n70.0\n120.0\n130.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Finally, write your... | |
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{
"role": "user",
"content": "<image>As shown in the figure , B O and C O bisect angle A B C and angle A C B respectively , M N parallel B C , if A B = N_0 , A C = N_1 , then the perimeter of triangle A M N is ()\n\nChoices:\n60.0\n66.0\n72.0\n78.0\n\nFirst, the purpose of the problem. Then, provide a descr... | |
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{
"role": "user",
"content": "<image>As shown in the figure , circle O is the circumscribed circle of triangle A B C , if angle A B C = N_0 , then the degree of angle A O C is ()\n\nChoices:\n20.0\n40.0\n60.0\n80.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your r... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , angle A = N_0 , point D is on the edge of A C , D E parallel B C , if angle 1 = N_1 , then the degree of angle B is ()\n\nChoices:\n35.0\n25.0\n45.0\n55.0\n\nFirst, the purpose of the problem. Then, provide a description. Next... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the measured B D = \"N_0\" , D C = \"N_1\" , E C = \"N_2\" , then width of the river A B is () .\n\nChoices:\n120.0\n100.0\n75.0\n25.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by s... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , angle C = N_0 , point D is on the edge of A C , D E parallel A B , if angle A D E = N_1 , then the degree of angle B is ()\n\nChoices:\n34.0\n44.0\n46.0\n54.0\n\nFirst, the purpose of the problem. Then, provide a description. ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , put the two vertices of a right triangle containing N_0 on the opposite sides of the ruler . If angle 1 = N_1 , then the degree of angle 2 is ()\n\nChoices:\n15.0\n20.0\n25.0\n30.0\n\nFirst, the purpose of the problem. Then, provide a description... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A B parallel C D , A F intersects C D at point O , and O F bisects angle E O D , if angle A = N_0 , then the degree of angle E O D is ()\n\nChoices:\n34.0\n68.0\n102.0\n146.0\n\nFirst, the purpose of the problem. Then, provide a description. Next... | |
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{
"role": "user",
"content": "<image>Put a ruler and a triangle plate as shown in the figure , if angle 1 = N_0 , then the degree of angle 2 is ()\n\nChoices:\n125.0\n120.0\n140.0\n130.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Final... | |
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{
"role": "user",
"content": "<image>In an activity class , the two study groups A and B measured some objects in the campus at the same time in the sun . The following is some information they obtained through the measurement : As shown in Figure 1 , the group A measured a piece of upright In Pingdi , the ... | |
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"role": "user",
"content": "<image>As shown in the figure , the quadrilateral A B C D is the inscribed quadrilateral of circle O , if angle B C D = N_0 , then the degree of angle B A D is ()\n\nChoices:\n140.0\n110.0\n90.0\n70.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, thin... | |
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{
"role": "user",
"content": "<image>As shown in the figure , it is known that A B parallel C D , E A is the bisector of angle C E B , if angle B E D = N_0 , then the degree of angle A is ()\n\nChoices:\n40.0\n50.0\n70.0\n80.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think th... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A B parallel C D , point E is on the extended line of C B . If angle A B E = N_0 , then the degree of angle E C D is ()\n\nChoices:\n20.0\n70.0\n100.0\n110.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through y... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the length of the generatrix of the cone mold is N_0 , and the radius of the bottom surface is N_1 , then the lateral area of the cone mold is ()\n\nChoices:\n31.41592653589793\n157.07963267948966\n314.1592653589793\n471.23889803846896\n\nFirst... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the three vertices of triangle A B C are on the straight lines a and b , and a parallel b . If angle 1 = N_0 , angle 2 = N_1 , then the degree of angle 3 is ()\n\nChoices:\n40.0\n60.0\n80.0\n120.0\n\nFirst, the purpose of the problem. Then, provi... | |
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{
"role": "user",
"content": "<image>As shown in the figure , it is known that A B parallel C D , A D bisects angle B A E , angle D = N_0 , then the degree of angle A E C is ()\n\nChoices:\n19.0\n38.0\n72.0\n76.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your rea... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , point D is on B C , A B = A D = D C , angle B = N_0 , then the degree of angle C is ()\n\nChoices:\n30.0\n40.0\n45.0\n60.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning s... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in the circle inscribed in the quadrilateral A B C D , if angle C = N_0 , then angle A is equal to ()\n\nChoices:\n120.0\n100.0\n80.0\n90.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , angle A B C = N_0 , angle A C B = N_1 , B P bisects angle A B C , C P bisects angle A C B , then the size of angle B P C is ()\n\nChoices:\n100.0\n110.0\n115.0\n120.0\n\nFirst, the purpose of the problem. Then, provide a descr... | |
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{
"role": "user",
"content": "<image>As shown in the figure , it is known that A B is the diameter of the circumscribed circle of triangle A B C , angle A = N_0 , then the degree of angle B is ()\n\nChoices:\n35.0\n45.0\n55.0\n65.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, thi... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the straight line A B parallel C D , if angle 1 = N_0 , then the degree of angle B O F is ()\n\nChoices:\n70.0\n100.0\n110.0\n120.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step... | |
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{
"role": "user",
"content": "<image>As shown in the figure , put the right angle vertex of the triangle on one side of the ruler , if angle 1 = N_0 , then the degree of angle 2 is ()\n\nChoices:\n10.0\n15.0\n20.0\n25.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through y... | |
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{
"role": "user",
"content": "<image>As shown in the figure , triangle A B C congruent triangle D C B , the corresponding vertices of points A and B are points D and C , respectively . If A B = N_0 , B C = N_1 , A C = N_2 , then the length of B D is ()\n\nChoices:\n7.0\n9.0\n12.0\nNone\n\nFirst, the purpose... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , the bisector of angle A B C and the outer bisector of angle A C B intersect at point D , angle A = N_0 , then angle D = ()\n\nChoices:\n15.0\n20.0\n25.0\n30.0\n\nFirst, the purpose of the problem. Then, provide a description. ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , it is known that A F bisects angle B A C , and F is used as F D perpendicular B C . If angle B is larger than angle C by N_0 degrees , then the degree of angle F is ()\n\nChoices:\n10.0\n15.0\n20.0\nNone\n\nFirst, the purpose of the problem. Then... | |
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"role": "user",
"content": "<image>As shown in the figure , triangle A B C congruent triangle B A D , point A and point B , point C and point D are corresponding points . If A B = N_0 cm , B D = N_1 cm , A D = N_2 cm , then the length of B C is ()\n\nChoices:\n6.0\n5.0\n4.0\nNone\n\nFirst, the purpose of ... | |
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"role": "user",
"content": "<image>As shown in the figure , A , B , C , D , E , F are N_0 points on the plane , then the degree of angle A + angle B + angle C + angle D + angle E + angle F is ()\n\nChoices:\n180.0\n360.0\n540.0\n720.0\n\nFirst, the purpose of the problem. Then, provide a description. Next... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A B parallel C D , B C parallel D E , if angle B = N_0 , then the degree of angle D is ()\n\nChoices:\n40.0\n140.0\n160.0\n60.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Fi... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the angle bisectors B O and C O of triangle A B C intersect at point O , angle A = N_0 , then angle B O C = ()\n\nChoices:\n150.0\n140.0\n130.0\n120.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your rea... | |
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{
"role": "user",
"content": "<image>As shown in the figure , B D is the diameter of circle O , angle A = N_0 , then the degree of angle C B D is ()\n\nChoices:\n30.0\n45.0\n60.0\n80.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Finally... | |
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{
"role": "user",
"content": "<image>As shown in the figure , an ant climbs from point A of the rectangular parallelepiped carton with length and width N_0 and height N_1 to point B along the surface of the carton , then the length of the shortest route it travels is ()\n\nChoices:\n11.0\n10.0\n14.0\nNone\n... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in the quadrilateral A B C D , angle A + angle B = N_0 , the bisector of angle A D C and angle D C B intersect at point O , then the degree of angle C O D is ()\n\nChoices:\n80.0\n90.0\n100.0\n110.0\n\nFirst, the purpose of the problem. Then, pro... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A B is the diameter of circle O , C and D are two points on circle O , C D perpendicular A B , if angle D A B = N_0 , then angle A O C is equal to ()\n\nChoices:\n25.0\n30.0\n50.0\n65.0\n\nFirst, the purpose of the problem. Then, provide a descri... | |
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{
"role": "user",
"content": "<image>As shown in the figure , points A , B , and C are all on circle O , angle A C B = N_0 , then the degree of angle A O B is ()\n\nChoices:\n20.0\n40.0\n60.0\n70.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , a pair of two right triangle plates with angles N_0 and N_1 respectively are assembled into the following figure , where angle C = N_2 , angle B = N_3 , angle E = N_4 , then the degree of angle B F D is ()\n\nChoices:\n15.0\n25.0\n30.0\n10.0\n\nF... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A C B , angle A C B = N_0 , angle A = N_1 , D is a point on A B . Fold triangle A B C along C D so that point B falls at B′ on the edge of A C , then angle A D B ′ is equal to ()\n\nChoices:\n25.0\n30.0\n35.0\n40.0\n\nFirst, the purpo... | |
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"role": "user",
"content": "<image>As shown in the figure , when a road is repaired to the lake , it needs to turn around the lake . If the first angle angle A is N_0 , the second angle angle B is N_1 , and the third angle is angle C , at this time the road is exactly parallel to the road before the first... | |
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"role": "user",
"content": "<image>As shown in the figure , B E and C F are the angular bisectors of triangle A B C , angle A B C = N_0 , angle A C B = N_1 , B E and C F intersect at D , then the degree of angle C D E is ()\n\nChoices:\n110.0\n70.0\n80.0\n75.0\n\nFirst, the purpose of the problem. Then, p... | |
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{
"role": "user",
"content": "<image>As shown in the figure , D E is the perpendicular bisector of A C in triangle A B C , if B C = N_0 , A B = N_1 , then the perimeter of triangle A B D is ()\n\nChoices:\n16.0\n18.0\n26.0\n28.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the quadrilateral A B C D is inscribed in circle O , and E is a point on the extended line of C D . If angle A D E = N_0 , then angle B is equal to ()\n\nChoices:\n130.0\n120.0\n80.0\n60.0\n\nFirst, the purpose of the problem. Then, provide a des... | |
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{
"role": "user",
"content": "<image>As shown in the figure , the C island is in the N_0 degrees of the north by east of the A island , and the C island is in the N_1 degrees of the north by west of the B island . The angle of view angle A C B of the two islands A and B from the C island is ()\n\nChoices:\n... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , B E and C F are the angular bisectors of angle A B C and angle A C B respectively , angle A = N_0 , then the degree of angle B D C is ()\n\nChoices:\n105.0\n115.0\n125.0\n135.0\n\nFirst, the purpose of the problem. Then, provi... | |
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{
"role": "user",
"content": "<image>As shown in the figure , A B parallel C D , E F perpendicular A B is in E , E F crosses C D in F , it is known that angle 1 = N_0 , then angle 2 = ()\n\nChoices:\n40.0\n50.0\n60.0\n130.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think throu... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , angle C = N_0 , point D is on the edge of B C , D E parallel A B , if angle C D E = N_1 , then the degree of angle A is ()\n\nChoices:\n30.0\n60.0\n120.0\n150.0\n\nFirst, the purpose of the problem. Then, provide a description... | |
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{
"role": "user",
"content": "<image>As shown in the figure , Xiao Cong puts the two vertices of a right triangle plate containing N_0 angles on the opposite sides of the ruler , and measured angle 1 = N_1 , then the degree of angle 2 is ()\n\nChoices:\n23.0\n22.0\n37.0\n67.0\n\nFirst, the purpose of the pr... | |
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{
"role": "user",
"content": "<image>Place a pair of right triangular plates as shown in the figure , so that a leg of the triangular plate with angle N_0 and a leg of the triangular plate with angle N_1 coincide , then the degree of angle 1 is ()\n\nChoices:\n45.0\n60.0\n75.0\n85.0\n\nFirst, the purpose of... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the straight line m parallel n , A B perpendicular m , angle A B C = N_0 , then angle ɑ is ()\n\nChoices:\n60.0\n50.0\n40.0\n30.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. ... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , it is known that the angle between the diameter A B of circle O and the chord A C is N_0 , and the tangent line P C passing through the point C and the extended line of A B intersect at the point P , then angle P is equal to ()\n\nChoices:\n15.0\... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , A D is the angle bisector of triangle A B C , B E is the height of triangle A B C , angle C = N_0 , angle A B C = N_1 , then angle 3 is ()\n\nChoices:\n59.0\n60.0\n56.0\n22.0\n\nFirst, the purpose of the problem. Then, provide... | |
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{
"role": "user",
"content": "<image>As shown in the figure , B C is the diameter of circle O , A D perpendicular B C , if angle D = N_0 , then the degree of angle B A D is ()\n\nChoices:\n72.0\n54.0\n45.0\n36.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reas... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the line segment A B is the diameter of circle O , the chord C D perpendicular A B , angle C A B = N_0 , then angle A O D is equal to ()\n\nChoices:\n155.0\n140.0\n130.0\n110.0\n\nFirst, the purpose of the problem. Then, provide a description. Ne... | |
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{
"role": "user",
"content": "<image>As shown in the figure , circle O is the circumscribed circle of triangle A B C , it is known that angle O A B = N_0 , then angle A C B is ()\n\nChoices:\n50.0\n60.0\n70.0\n80.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your r... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the straight line a parallel b , the right triangle is placed as shown , angle D C B = N_0 , if angle 2 + angle B = N_1 , then the degree of angle 1 is ()\n\nChoices:\n40.0\n30.0\n25.0\n20.0\n\nFirst, the purpose of the problem. Then, provide a d... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , two points A and B are located at both ends of a pond . Xiao Cong wants to use a rope to measure the distance between A and B , but the rope is not long enough . A classmate helped him think of an idea : first take one on the ground . Go directly... | |
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{
"role": "user",
"content": "<image>As shown in the figure , point P is outside circle O , P A and P B are tangent to circle O at points A and B respectively , angle P = N_0 , then angle A O B is equal to ()\n\nChoices:\n150.0\n130.0\n155.0\n135.0\n\nFirst, the purpose of the problem. Then, provide a descr... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the straight line a parallel b , the radial line D C intersects the straight line a at point C , and passes through point D as D E perpendicular b at point E . It is known that angle 1 = N_0 , then the degree of angle 2 is ()\n\nChoices:\n115.0\n... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the straight line a parallel b , angle 1 = N_0 , angle 2 = N_1 , then the degree of angle 3 is ()\n\nChoices:\n75.0\n55.0\n40.0\n35.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by st... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , A B = A D = D C , angle B = N_0 , then the degree of angle C is ()\n\nChoices:\n35.0\n40.0\n45.0\n50.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. Finally... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , A B is the diameter of circle O , C and D are two points on circle O , if angle A B C = N_0 , then the degree of angle B D C is ()\n\nChoices:\n40.0\n30.0\n20.0\n10.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think ... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the short arm O A of the railing at the railway crossing is long N_0 , and the long arm O B is long N_1 . When the outer end A of the short arm drops by N_2 , the outer end B of the long arm rises ()\n\nChoices:\n2.0\n4.0\n4.5\n8.0\n\nFirst, the ... | |
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{
"role": "user",
"content": "<image>Figure 1 shows a quadrilateral A B C D paper sheet , where angle B = N_0 , angle C = N_1 . If C D is superimposed on A B , a fold line M N appears , and then after the paper is unfolded , the two points M and N are on A D and B C respectively , as shown in Figure 2 , the... | |
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{
"role": "user",
"content": "<image>As shown in the figure , P A and P B are the tangent lines of circle O , points A and B are the points of tangency , A C is the diameter of circle O , given that angle P = N_0 , then the size of angle A C B is ()\n\nChoices:\n60.0\n65.0\n70.0\n75.0\n\nFirst, the purpose ... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the straight line a parallel b , angle 1 = N_0 , angle 2 = N_1 , then angle 3 is equal to ()\n\nChoices:\n40.0\n60.0\n80.0\n100.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step by step. ... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , A B and C D are both chords of circle O , and A B perpendicular C D , if angle C D B = N_0 , then the size of angle A C D is ()\n\nChoices:\n28.0\n31.0\n38.0\n62.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think thr... | |
[
{
"role": "user",
"content": "<image>Place an isosceles right triangle board and a ruler as shown in the figure , if angle 1 = N_0 , then the degree of angle 2 is ()\n\nChoices:\n85.0\n75.0\n60.0\n45.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning step... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , A B parallel C D , the straight line E F intersects A B and C D at points E and F respectively . If angle A E F = N_0 , then the degree of angle E F D is ()\n\nChoices:\n20.0\n40.0\n50.0\n140.0\n\nFirst, the purpose of the problem. Then, provide ... | |
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{
"role": "user",
"content": "<image>As shown in the figure , in triangle A B C , angle B = N_0 , angle C = N_1 , extend B A to point D , then the size of angle C A D is ()\n\nChoices:\n110.0\n80.0\n70.0\n60.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reason... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , the quadrilateral A B C D is the inscribed quadrilateral of circle O , if angle A = N_0 , then the degree of angle C is ()\n\nChoices:\n100.0\n110.0\n120.0\n130.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think thro... | |
[
{
"role": "user",
"content": "<image>As shown in the figure , A B is the chord of circle O , if C is a point on circle O , angle C = N_0 , then angle O B A is equal to ()\n\nChoices:\n30.0\n40.0\n45.0\n60.0\n\nFirst, the purpose of the problem. Then, provide a description. Next, think through your reasoning... |
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