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1
| ability
stringclasses 2
values | reward_model
dict | extra_info
dict |
|---|---|---|---|---|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-7, -10), B=(-2, -3), and C=(-3, -6), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "17.10°",
"style": "rule"
}
|
{
"index": 0,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-1, -6), B=(4, 1), and C=(-7, 4). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.905",
"style": "rule"
}
|
{
"index": 1,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(6, 7), B=(-7, -5), and C=(2, -3), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(10.195, -11.878)",
"style": "rule"
}
|
{
"index": 2,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(3, 5), B=(-2, -8), and C=(-1, 0), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-22.185, 8.148)",
"style": "rule"
}
|
{
"index": 3,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(2, -9), B=(8, 8), and C=(-3, 10). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "4.073",
"style": "rule"
}
|
{
"index": 4,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-8, 3), B=(7, 4), and C=(8, 0), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(7.541, 6.885)",
"style": "rule"
}
|
{
"index": 5,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(0, -6), B=(7, 7), and C=(-1, 6), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "54.57°",
"style": "rule"
}
|
{
"index": 6,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(1, 3), B=(-7, 0), and C=(7, 6). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.197",
"style": "rule"
}
|
{
"index": 7,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-2, 1), B=(10, -3), and C=(5, 0), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(14.500, 28.500)",
"style": "rule"
}
|
{
"index": 8,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(6, 7), B=(-5, -3), and C=(-3, 7). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.642",
"style": "rule"
}
|
{
"index": 9,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-9, 6), B=(5, 1), and C=(3, -9), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(7.200, 2.760)",
"style": "rule"
}
|
{
"index": 10,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-4, 4), B=(6, 5), and C=(6, 1), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "84.29°",
"style": "rule"
}
|
{
"index": 11,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(4, 7), B=(-1, 5), and C=(5, 2). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.570",
"style": "rule"
}
|
{
"index": 12,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-4, -6), B=(-1, -8), and C=(-5, -1). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.775",
"style": "rule"
}
|
{
"index": 13,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-10, 5), B=(10, 6), and C=(-1, 7), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "8.06°",
"style": "rule"
}
|
{
"index": 14,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(1, 8), B=(9, -10), and C=(-3, 6). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.992",
"style": "rule"
}
|
{
"index": 15,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(4, 2), B=(1, -1), and C=(-2, 4), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "75.96°",
"style": "rule"
}
|
{
"index": 16,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-8, 10), B=(4, -10), and C=(-6, -1). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.918",
"style": "rule"
}
|
{
"index": 17,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-1, 8), B=(-6, -2), and C=(-3, 5), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-57.000, 32.000)",
"style": "rule"
}
|
{
"index": 18,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-5, 7), B=(-4, 0), and C=(-1, 0), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-5.000, -0.571)",
"style": "rule"
}
|
{
"index": 19,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-5, -8), B=(-3, 4), and C=(-1, 1), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "43.15°",
"style": "rule"
}
|
{
"index": 20,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(4, -1), B=(-2, 5), and C=(-8, 2), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-1.000, 9.000)",
"style": "rule"
}
|
{
"index": 21,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-7, 10), B=(9, 2), and C=(7, -10), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(15.154, 6.308)",
"style": "rule"
}
|
{
"index": 22,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-1, -1), B=(6, -3), and C=(4, 4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(2.889, 0.111)",
"style": "rule"
}
|
{
"index": 23,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-1, 3), B=(-3, 4), and C=(-1, -2). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.737",
"style": "rule"
}
|
{
"index": 24,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-7, 3), B=(4, 3), and C=(-2, 9). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.418",
"style": "rule"
}
|
{
"index": 25,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(4, 6), B=(-7, 9), and C=(8, -3), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "23.40°",
"style": "rule"
}
|
{
"index": 26,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-9, -7), B=(-5, -8), and C=(9, 1), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "133.23°",
"style": "rule"
}
|
{
"index": 27,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-1, 4), B=(4, -6), and C=(0, -7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.708",
"style": "rule"
}
|
{
"index": 28,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(6, 9), B=(-10, -2), and C=(-6, -4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-2.816, -8.632)",
"style": "rule"
}
|
{
"index": 29,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(9, -5), B=(1, 7), and C=(9, 1). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.578",
"style": "rule"
}
|
{
"index": 30,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-7, 6), B=(5, 8), and C=(-5, 4), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-4.143, -1.143)",
"style": "rule"
}
|
{
"index": 31,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(6, -7), B=(0, -7), and C=(-1, -5), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "116.57°",
"style": "rule"
}
|
{
"index": 32,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(8, 3), B=(4, -9), and C=(6, 5), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(15.000, 2.000)",
"style": "rule"
}
|
{
"index": 33,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(4, 2), B=(-4, -1), and C=(-9, 3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-4.596, -8.745)",
"style": "rule"
}
|
{
"index": 34,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(0, -4), B=(-3, -4), and C=(-7, -1), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-7.000, -13.333)",
"style": "rule"
}
|
{
"index": 35,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-7, -1), B=(-2, 3), and C=(-9, 10). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.292",
"style": "rule"
}
|
{
"index": 36,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(4, 1), B=(9, -5), and C=(-3, -3). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.211",
"style": "rule"
}
|
{
"index": 37,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(2, 7), B=(3, 1), and C=(1, 7), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(3.000, 7.333)",
"style": "rule"
}
|
{
"index": 38,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(4, 0), B=(7, 7), and C=(2, 5), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "45.00°",
"style": "rule"
}
|
{
"index": 39,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(5, 6), B=(-1, -5), and C=(-5, -2). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.044",
"style": "rule"
}
|
{
"index": 40,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(4, -8), B=(-6, 2), and C=(-9, -9), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-5.429, -5.429)",
"style": "rule"
}
|
{
"index": 41,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-1, -9), B=(5, -10), and C=(6, 0), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "86.25°",
"style": "rule"
}
|
{
"index": 42,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(9, -7), B=(0, -4), and C=(-3, 4). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.836",
"style": "rule"
}
|
{
"index": 43,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(7, 0), B=(-10, -8), and C=(6, 10). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "3.363",
"style": "rule"
}
|
{
"index": 44,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-4, 7), B=(-7, -2), and C=(0, 10). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.951",
"style": "rule"
}
|
{
"index": 45,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-4, 0), B=(-5, 10), and C=(-10, 6), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-8.889, 6.111)",
"style": "rule"
}
|
{
"index": 46,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(9, -2), B=(-6, 1), and C=(-8, -6). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.772",
"style": "rule"
}
|
{
"index": 47,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-8, 5), B=(8, 8), and C=(-1, 10). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.730",
"style": "rule"
}
|
{
"index": 48,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(8, -5), B=(-5, 2), and C=(4, 4). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.631",
"style": "rule"
}
|
{
"index": 49,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(6, 8), B=(7, 7), and C=(8, -2), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(19.500, 9.500)",
"style": "rule"
}
|
{
"index": 50,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(8, 1), B=(-7, -8), and C=(1, -6), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(16.000, -31.000)",
"style": "rule"
}
|
{
"index": 51,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-5, -7), B=(-2, -1), and C=(3, -10), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "55.62°",
"style": "rule"
}
|
{
"index": 52,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(6, 7), B=(-6, 5), and C=(-10, -6), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "119.45°",
"style": "rule"
}
|
{
"index": 53,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(0, 2), B=(-4, -7), and C=(0, -9), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-4.500, -7.000)",
"style": "rule"
}
|
{
"index": 54,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(3, 1), B=(-9, 8), and C=(-10, 7). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.641",
"style": "rule"
}
|
{
"index": 55,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(8, -9), B=(1, 3), and C=(-9, 5), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(13.415, 18.075)",
"style": "rule"
}
|
{
"index": 56,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(2, -4), B=(9, -5), and C=(-3, -3), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-34.000, -220.000)",
"style": "rule"
}
|
{
"index": 57,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(4, 4), B=(-5, 2), and C=(1, 3). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.162",
"style": "rule"
}
|
{
"index": 58,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-4, 7), B=(1, 4), and C=(-9, 6), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "19.65°",
"style": "rule"
}
|
{
"index": 59,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(9, 1), B=(-5, 7), and C=(9, -5). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.117",
"style": "rule"
}
|
{
"index": 60,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(4, -4), B=(-8, 9), and C=(-7, 10), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "92.29°",
"style": "rule"
}
|
{
"index": 61,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-10, -5), B=(-7, -6), and C=(-7, -8). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.638",
"style": "rule"
}
|
{
"index": 62,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(1, 8), B=(-7, -10), and C=(-1, 6), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "3.41°",
"style": "rule"
}
|
{
"index": 63,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(5, -10), B=(7, 6), and C=(5, -9), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.47°",
"style": "rule"
}
|
{
"index": 64,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(9, 8), B=(3, 5), and C=(-1, -6). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.516",
"style": "rule"
}
|
{
"index": 65,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-8, 2), B=(-2, 2), and C=(-4, -8). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.225",
"style": "rule"
}
|
{
"index": 66,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-3, 4), B=(4, 7), and C=(-9, -7), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-20.797, 20.525)",
"style": "rule"
}
|
{
"index": 67,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(9, -3), B=(3, 5), and C=(-2, 10), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(94.000, 82.000)",
"style": "rule"
}
|
{
"index": 68,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(0, 5), B=(-4, 2), and C=(3, 9). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.352",
"style": "rule"
}
|
{
"index": 69,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(8, 9), B=(-1, 4), and C=(3, -5), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-2.248, 4.446)",
"style": "rule"
}
|
{
"index": 70,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(10, -2), B=(-10, 5), and C=(7, 1). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.909",
"style": "rule"
}
|
{
"index": 71,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(8, -7), B=(0, -3), and C=(10, 9). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "3.342",
"style": "rule"
}
|
{
"index": 72,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-4, -7), B=(7, -7), and C=(0, 7), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(0.000, -5.000)",
"style": "rule"
}
|
{
"index": 73,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(9, 7), B=(-1, -10), and C=(10, -7), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "44.28°",
"style": "rule"
}
|
{
"index": 74,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-5, -5), B=(-4, 2), and C=(-5, 7). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.496",
"style": "rule"
}
|
{
"index": 75,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(10, -5), B=(-1, -7), and C=(1, -1), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "61.26°",
"style": "rule"
}
|
{
"index": 76,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-5, 7), B=(7, 3), and C=(-7, -8), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-2.894, 4.319)",
"style": "rule"
}
|
{
"index": 77,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-3, -4), B=(10, 8), and C=(4, -8), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "26.73°",
"style": "rule"
}
|
{
"index": 78,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-4, 8), B=(2, 10), and C=(-5, 9). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.540",
"style": "rule"
}
|
{
"index": 79,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(-4, 9), B=(-1, -8), and C=(1, -3), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "31.81°",
"style": "rule"
}
|
{
"index": 80,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-2, -8), B=(3, -2), and C=(-7, -9). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.995",
"style": "rule"
}
|
{
"index": 81,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(7, -10), B=(-5, -9), and C=(3, -2), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(2.739, -5.130)",
"style": "rule"
}
|
{
"index": 82,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-3, 9), B=(-1, 8), and C=(-5, 1). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.971",
"style": "rule"
}
|
{
"index": 83,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-9, 8), B=(9, 4), and C=(-3, 10), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "14.04°",
"style": "rule"
}
|
{
"index": 84,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(9, 8), B=(8, -7), and C=(-10, -10). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "4.491",
"style": "rule"
}
|
{
"index": 85,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(2, 6), B=(1, -6), and C=(5, -10). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.530",
"style": "rule"
}
|
{
"index": 86,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(6, -2), B=(-9, 2), and C=(10, -3), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.19°",
"style": "rule"
}
|
{
"index": 87,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(3, -2), B=(4, 10), and C=(4, -10), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "4.76°",
"style": "rule"
}
|
{
"index": 88,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(1, 6), B=(-8, 2), and C=(-1, -10), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-6.235, 1.779)",
"style": "rule"
}
|
{
"index": 89,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-6, 3), B=(-9, -5), and C=(-9, -1), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-19.667, 3.000)",
"style": "rule"
}
|
{
"index": 90,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(1, 5), B=(0, 9), and C=(0, 7), find the coordinates of its orthocenter. Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(-8.000, 5.000)",
"style": "rule"
}
|
{
"index": 91,
"split": "train"
}
|
advanced_geometry/orthocenter
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(6, -4), B=(7, 10), and C=(-6, -10), determine the orthocenter (intersection of altitudes). Show your work in <think> </think> tags. Round the coordinates to 3 decimal places and return them inside parenthesis in <answer> </answer>, for example <answer> (0.304, 1.217) </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "(17.852, -11.704)",
"style": "rule"
}
|
{
"index": 92,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(1, 10), B=(10, 8), and C=(-2, 5), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "26.57°",
"style": "rule"
}
|
{
"index": 93,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nGiven a triangle with vertices A=(3, 6), B=(-9, 3), and C=(5, -4), determine the angle at B in degrees. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "40.60°",
"style": "rule"
}
|
{
"index": 94,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-5, 3), B=(0, -4), and C=(-3, 5). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "1.147",
"style": "rule"
}
|
{
"index": 95,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(2, 4), B=(-1, -4), and C=(6, -2). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "2.171",
"style": "rule"
}
|
{
"index": 96,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(9, 7), B=(9, -1), and C=(7, -10). Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.466",
"style": "rule"
}
|
{
"index": 97,
"split": "train"
}
|
advanced_geometry/incircle_radius
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-10, -2), B=(-10, 7), and C=(-9, -3). Compute the radius of its incircle. Show your work in <think> </think> tags. Round the radius to 3 decimal places and return it in <answer> </answer> tags, for example <answer> 2.176 </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "0.440",
"style": "rule"
}
|
{
"index": 98,
"split": "train"
}
|
advanced_geometry/angle_measure
|
[
{
"content": "<|im_start|>system\nYou are a helpful assistant. You first thinks about the reasoning process in the mind and then provides the user with the answer.<|im_end|>\n<|im_start|>user\nIn triangle ABC with coordinates A=(-10, 8), B=(5, -5), and C=(8, 4), find the measure (in degrees) of angle ABC. Show your work in <think> </think> tags. Round the angle degrees to 2 decimal places, append a degree symbol, and return it in <answer> </answer> tags, for example <answer> 17.10° </answer>.<|im_end|>\n<|im_start|>assistant\nLet me solve this step by step.\n<think>",
"role": "user"
}
] |
deductive, inductive
|
{
"ground_truth": "67.52°",
"style": "rule"
}
|
{
"index": 99,
"split": "train"
}
|
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