images listlengths 0 0 | conversations listlengths 2 2 | id stringlengths 1 5 | source_dataset stringclasses 1
value |
|---|---|---|---|
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that circle O is the circumscribed circle of triangle ABC, and AB is the diameter of circle O, if OC = 5.0, AC = 6.0, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:无法确定\n\nYou first think thr... | 900 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, if OC = 5.0, AC = 6.0, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:无法确定\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide y... | 901 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, if OC = 5.0, AC = 6.0, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:无法确定\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide y... | 902 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the length of BC is ()\nChoices:\nA:10\nB:9\nC:8\nD:no solution\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer... | 903 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To determine the length o... | 904 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, angle XOY = 45.0, the two vertices A and B of a right triangle ABC move on OX and OY respectively, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8√{2... | 905 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, angle XOY = 45.0, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8√{2}\nD:10√{2}\n\nYou first think through the reasoning process as an internal monol... | 906 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, angle XOY = 45.0, where AB = 10.0, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8√{2}\nD:10√{2}\n\nYou first think through the reasoning process as an internal monol... | 907 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the maximum value of the distance from point O to vertex A is ()\nChoices:\nA:8\nB:10\nC:8√{2}\nD:10√{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </thi... | 908 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To determine the maximum ... | 909 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that the angle between the diameter AB of circle O and the chord AC is 30.0, the tangent PC passing through point C and the extended line of AB intersect at point P, the radius of circle O is 2.0, then ... | 910 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the radius of circle O is 2.0, then PC is ()\nChoices:\nA:4\nB:4√{3}\nC:6\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide you... | 911 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the radius of circle O is 2.0, then PC is ()\nChoices:\nA:4\nB:4√{3}\nC:6\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide you... | 912 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then PC is ()\nChoices:\nA:4\nB:4√{3}\nC:6\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within ... | 913 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nGiven a diameter... | 914 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, in the circle O with a radius of 2.0, C is a point on the extended line of the diameter AB, CD is tangent to the circle at point D. Connect AD, given that angle DAC = 30.0, the length of the line segment CD is ()\n... | 915 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, in the circle O with a radius of 2.0, given that angle DAC = 30.0, the length of the line segment CD is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:2√{3}\n\nYou first think through the reasoning process as an internal monolo... | 916 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, in the circle O with a radius of 2.0, given that angle DAC = 30.0, the length of the line segment CD is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:2√{3}\n\nYou first think through the reasoning process as an internal monolo... | 917 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, CD is tangent to the circle at point D, the length of the line segment CD is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think... | 918 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo solve for the... | 919 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, draw a tangent of circle O through any point P on the straight line L , and the tangent point is Q; if PQ is taken as the edge ... | 920 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, then the minimum area of the square PQRS is ()\nChoices:\nA:7\nB:8\nC:9\nD:10\n\nYou first think through the reasoning process ... | 921 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, Circle O is a circle with a radius of 1.0, the distance from point O to line L is 3.0, then the minimum area of the square PQRS is ()\nChoices:\nA:7\nB:8\nC:9\nD:10\n\nYou first think through the reasoning process ... | 922 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, then the minimum area of the square PQRS is ()\nChoices:\nA:7\nB:8\nC:9\nD:10\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your fin... | 923 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nIn the given fig... | 924 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB is the diameter of circle O, C is the point on circle O, passing point C is the tangent of circle O and intersects the extended line of AB at point E, OD perpendicular AC at point D, if angle E = 30.0, CE = 6.0... | 925 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, OD perpendicular AC at point D, if angle E = 30.0, CE = 6.0, then the value of OD is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed with... | 926 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, if angle E = 30.0, CE = 6.0, then the value of OD is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, p... | 927 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, passing point C is the tangent of circle O, then the value of OD is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think... | 928 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo solve this pr... | 929 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the straight line AB is tangent to circle O at point A, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:√{3}\nD:2√{3}\n\nYou first think through the reasoning ... | 930 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:√{3}\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think... | 931 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the radius of circle O is 1.0, if angle OBA = 30.0, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:√{3}\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think... | 932 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the straight line AB is tangent to circle O at point A, then the length of OB is ()\nChoices:\nA:1\nB:2\nC:√{3}\nD:2√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <t... | 933 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nIn the given pro... | 934 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that BA is the tangent of circle O, and connect OB to intersect circle O at point C. If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()\nChoices:\nA:2√{2}-1\nB:√{2}\nC:2√{2}-2\nD... | 935 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()\nChoices:\nA:2√{2}-1\nB:√{2}\nC:2√{2}-2\nD:2-√{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed withi... | 936 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, If angle B = 45.0 and the length of AB is 2.0, then the length of BC is ()\nChoices:\nA:2√{2}-1\nB:√{2}\nC:2√{2}-2\nD:2-√{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed withi... | 937 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, it is known that BA is the tangent of circle O, then the length of BC is ()\nChoices:\nA:2√{2}-1\nB:√{2}\nC:2√{2}-2\nD:2-√{2}\n\nYou first think through the reasoning process as an internal monologue, enclosed with... | 938 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nGiven that BA is... | 939 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, point A is a point outside circle O, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5... | 940 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5\nD:3\n\nYou first think through the ... | 941 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB, AC, and BD are the tangents of circle O, and the tangent points are P, C, and D respectively. If AB = 5.0, AC = 3.0, then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5\nD:3\n\nYou first think through the ... | 942 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, AB, AC, and BD are the tangents of circle O. then the length of BD is ()\nChoices:\nA:1.5\nB:2\nC:2.5\nD:3\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think>... | 943 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nGiven that AB, A... | 944 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, AC is the diameter of circle O, given that angle P = 50.0, then the size of angle ACB is ()\nChoices:\nA:65°\nB:60°\nC:55°\nD:50°\n\nYou first... | 945 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, PA and PB are tangents of circle O, the tangent point of point A and B, given that angle P = 50.0, then the size of angle ACB is ()\nChoices:\nA:65°\nB:60°\nC:55°\nD:50°\n\nYou first think through the reasoning pro... | 946 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, given that angle P = 50.0, then the size of angle ACB is ()\nChoices:\nA:65°\nB:60°\nC:55°\nD:50°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Th... | 947 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, PA and PB are tangents of circle O, then the size of angle ACB is ()\nChoices:\nA:65°\nB:60°\nC:55°\nD:50°\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think>... | 948 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nIn a tangential ... | 949 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, points A, B, and C are on circle O, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()\nChoices:\nA:3\nB:\\... | 950 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and the tangent line of circle O passing through point A intersects the extended line of OC at point P, angle B = 30.0, OP = 3.0, then the length of AP is ()\nChoices:\nA:3\nB:\\frac{3}{2}\nC:\\frac{2}{3}√{3}\nD:\\... | 951 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, angle B = 30.0, OP = 3.0, then the length of AP is ()\nChoices:\nA:3\nB:\\frac{3}{2}\nC:\\frac{2}{3}√{3}\nD:\\frac{3}{2}√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed withi... | 952 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, and the tangent line of circle O passing through point A, then the length of AP is ()\nChoices:\nA:3\nB:\\frac{3}{2}\nC:\\frac{2}{3}√{3}\nD:\\frac{3}{2}√{3}\n\nYou first think through the reasoning process as an in... | 953 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nIn a circle, the... | 954 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, point P is outside circle O. PA and PB are connected. the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()\nChoices:... | 955 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the straight lines PA and PB are the two tangents of circle O. If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()\nChoices:\nA:5\nB:10\nC:10√{3}\nD:5√{3}\n\nYou first think thro... | 956 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, If angle APB = 120.0, the radius of circle O is 10.0, then the length of chord AB is ()\nChoices:\nA:5\nB:10\nC:10√{3}\nD:5√{3}\n\nYou first think through the reasoning process as an internal monologue, enclosed wi... | 957 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the straight lines PA and PB are the two tangents of circle O, then the length of chord AB is ()\nChoices:\nA:5\nB:10\nC:10√{3}\nD:5√{3}\n\nYou first think through the reasoning process as an internal monologue, en... | 958 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "Let's start by considerin... | 959 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively, and the tangent point C is on the arc AB. If the length of PA is 2.0... | 960 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, PA and PB are tangent to circle O at points A and B respectively, the tangent EF of circle O intersects PA and PB at points E and F respectively. If the length of PA is 2.0, then the perimeter of triangle PEF is ()... | 961 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, if the length of PA is 2.0, then the perimeter of triangle PEF is ()\nChoices:\nA:8\nB:6\nC:4\nD:2\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. T... | 962 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, PA and PB are tangent to circle O, the tangent EF of circle O intersects PA and PB at points E and F respectively.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> ... | 963 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo solve the pro... | 964 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nPut the ruler, the triangle ruler and the round nut on the desktop as shown in the figure, angle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6√{3}cm\nD:12√{3}cm\n\nYou first think t... | 965 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAngle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6√{3}cm\nD:12√{3}cm\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tag... | 966 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAngle CAB = 60.0, if AD = 6.0, then the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6√{3}cm\nD:12√{3}cm\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tag... | 967 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThen the outer diameter of the round nut is ()\nChoices:\nA:12cm\nB:24cm\nC:6√{3}cm\nD:12√{3}cm\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final ans... | 968 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<stdinknowledge>\nTo dete... | 969 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, point P is a point on the extended line AB of the diameter of circle O, passing point P to draw the tangent PC of circle O, and the tangent point is C. If AO = OB = PB = 1.0, then the length of PC is ()\nChoices:\n... | 970 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, passing point P to draw the tangent PC of circle O, If AO = OB = PB = 1.0, then the length of PC is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:√{5}\n\nYou first think through the reasoning process as an internal monologue, ... | 971 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, If AO = OB = PB = 1.0, then the length of PC is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:√{5}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide... | 972 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, passing point P to draw the tangent PC of circle O, then the length of PC is ()\nChoices:\nA:1\nB:√{3}\nC:2\nD:√{5}\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think>... | 973 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "To determine the length o... | 974 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, a torus carpet is to be laid in the lobby of a hotel. The worker only measures the length of the chord AB of the great circle that is tangent to the small circle, and then calculates the area of the torus. If the... | 975 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the chord AB of the great circle is tangent to the small circle, if the measured length of AB is 8.0, the area of the torus is ()\nChoices:\nA:16平方米\nB:8π平方米\nC:64平方米\nD:16π平方米\n\nYou first think through the rea... | 976 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, if the measured length of AB is 8.0, the area of the torus is ()\nChoices:\nA:16平方米\nB:8π平方米\nC:64平方米\nD:16π平方米\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> <... | 977 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, the chord AB of the great circle is tangent to the small circle, the area of the torus is ()\nChoices:\nA:16m^2\nB:8πm^2\nC:64m^2\nD:16πm^2\n\nYou first think through the reasoning process as an internal monolog... | 978 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo find the area... | 979 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, circle O is the circumcircle of triangle ABC, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()\nChoices:\nA:6√{5}\nB:6√{3}\nC:6√{2}\nD:6\n\nYou first think throu... | 980 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, circle O ia tangent to AB at point C, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()\nChoices:\nA:6√{5}\nB:6√{3}\nC:6√{2}\nD:6\n\nYou first think through the reasoning process as an internal monolo... | 981 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, angle BCE = 60.0, DC = 6.0, DE = 4.0, then S_triangle CDE is ()\nChoices:\nA:6√{5}\nB:6√{3}\nC:6√{2}\nD:6\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> ... | 982 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nAs shown in the figure, circle O ia tangent to AB at point C, then S_triangle CDE is ()\nChoices:\nA:6√{5}\nB:6√{3}\nC:6√{2}\nD:6\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> ... | 983 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nTo find the area... | 984 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThere is an isosceles triangle with side length 13 and base length 10. Find the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </t... | 985 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThere is an isosceles triangle. Find the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final an... | 986 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nFind the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."... | 987 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThere is an isosceles triangle. Find the area of the figure.\nChoices:\nA:30\nB:60\nC:120\nD:240\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final an... | 988 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>To find the area o... | 989 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nCircle O has a radius of 13 inches, which is the length of O C. Radius O B is perpendicular at point X to chord C D which is 24 inches long. Find O X.\nChoices:\nA:5\nB:12\nC:13\nD:26\n\nYou first think through the reasoning process as an... | 990 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nCircle O has a radius of 13 inches. Chord C D is 24 inches long. Find O X.\nChoices:\nA:5\nB:12\nC:13\nD:26\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide yo... | 991 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nCircle O has a radius of 13 inches. Chord C D is 24 inches long. Find O X.\nChoices:\nA:5\nB:12\nC:13\nD:26\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide yo... | 992 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nFind O X.\nChoices:\nA:5\nB:12\nC:13\nD:26\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": ... | 993 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nThe problem is a... | 994 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThere is an isosceles triangle with side length 32. The base angle is 54 degrees. x is half of the base. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0\n\nYou first think through the reasoning process as an ... | 995 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThere is an isosceles triangle with side length 32. The base angle is 54 degrees. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0\n\nYou first think through the reasoning process as an internal monologue, enc... | 996 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThere is a triangle with side length 32. The base angle is 54 degrees. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0\n\nYou first think through the reasoning process as an internal monologue, enclosed withi... | 997 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nThere is an isosceles triangle. Find x. Round to the nearest tenth.\nChoices:\nA:18.8\nB:23.2\nC:25.9\nD:44.0\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide ... | 998 | AI4Math_MathVerse/baseline/rollout_8 |
[] | [
{
"from": "human",
"value": "System:\nYou are a helpful assistant.\n\nYou first think through the reasoning process as an internal monologue, enclosed within <think> </think> tags. Then, provide your final answer enclosed within \\boxed{}."
},
{
"from": "gpt",
"value": "<think>\nIn an isosceles ... | 999 | AI4Math_MathVerse/baseline/rollout_8 |
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