reasoning-gym
Collection
Datasets generated using https://github.com/open-thought/reasoning-gym (with Qwen3-instruct templates) • 15 items • Updated
data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2... | reasoning | {
"ground_truth": {
"entry": {
"answer": "17.10°",
"metadata": "{\"A\": [\"-7\", \"-10\"], \"B\": [\"-2\", \"-3\"], \"C\": [\"-3\", \"-6\"], \"angle_ABC_degrees\": 17.10272896905237, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 0... | {
"index": 0,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-1, -6), B=(4, 1), and C=(-7, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(0.304, -1.217)",
"metadata": "{\"A\": [\"-1\", \"-6\"], \"B\": [\"4\", \"1\"], \"C\": [\"-7\", \"4\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"7/23\", \"-28/23\"], \"orthocenter_approx\": [0.30434782608695654, -1.217391304347826... | {
"index": 1,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(6, 7), B=(-7, -5), and C=(2, -3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answe... | reasoning | {
"ground_truth": {
"entry": {
"answer": "2.176",
"metadata": "{\"A\": [\"6\", \"7\"], \"B\": [\"-7\", \"-5\"], \"C\": [\"2\", \"-3\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 2.176123777286009, \"incircle_radius_exact\": \"sqrt(-sqrt(29) + sqrt(85)/2 + sqr... | {
"index": 2,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(3, 5), B=(-2, -8), and C=(-1, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.951",
"metadata": "{\"A\": [\"3\", \"5\"], \"B\": [\"-2\", \"-8\"], \"C\": [\"-1\", \"0\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.9509128146769613, \"incircle_radius_exact\": \"sqrt(-sqrt(194)/2 + sqrt(41)/2 +... | {
"index": 3,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(2, -9), B=(8, 8), and C=(-3, 10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(4.945, 7.196)",
"metadata": "{\"A\": [\"2\", \"-9\"], \"B\": [\"8\", \"8\"], \"C\": [\"-3\", \"10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"984/199\", \"1432/199\"], \"orthocenter_approx\": [4.944723618090452, 7.19597989949748... | {
"index": 4,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-8, 3), B=(7, 4), and C=(8, 0). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.721",
"metadata": "{\"A\": [\"-8\", \"3\"], \"B\": [\"7\", \"4\"], \"C\": [\"8\", \"0\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.7214510174925386, \"incircle_radius_exact\": \"sqrt(-sqrt(17)/2 + sqrt(226)/2 + s... | {
"index": 5,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Rou... | reasoning | {
"ground_truth": {
"entry": {
"answer": "54.57°",
"metadata": "{\"A\": [\"0\", \"-6\"], \"B\": [\"7\", \"7\"], \"C\": [\"-1\", \"6\"], \"angle_ABC_degrees\": 54.57422788509182, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 6, \"t... | {
"index": 6,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(1, 3), B=(-7, 0), and C=(7, 6), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(58.000, -130.000)",
"metadata": "{\"A\": [\"1\", \"3\"], \"B\": [\"-7\", \"0\"], \"C\": [\"7\", \"6\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"58\", \"-130\"], \"orthocenter_approx\": [58.0, -130.0], \"source_dataset\": \"advan... | {
"index": 7,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-2, 1), B=(10, -3), and C=(5, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.626",
"metadata": "{\"A\": [\"-2\", \"1\"], \"B\": [\"10\", \"-3\"], \"C\": [\"5\", \"0\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.626195388715472, \"incircle_radius_exact\": \"sqrt(-2*sqrt(10) + sqrt(34)/2 + 5... | {
"index": 8,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(6, 7), B=(-5, -3), and C=(-3, 7), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-5.000, 9.200)",
"metadata": "{\"A\": [\"6\", \"7\"], \"B\": [\"-5\", \"-3\"], \"C\": [\"-3\", \"7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-5\", \"46/5\"], \"orthocenter_approx\": [-5.0, 9.2], \"source_dataset\": \"advanced_... | {
"index": 9,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-9, 6), B=(5, 1), and C=(3, -9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round... | reasoning | {
"ground_truth": {
"entry": {
"answer": "3.388",
"metadata": "{\"A\": [\"-9\", \"6\"], \"B\": [\"5\", \"1\"], \"C\": [\"3\", \"-9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 3.388032708309733, \"incircle_radius_exact\": \"sqrt(-sqrt(221)/2 + sqrt(26) + 3*s... | {
"index": 10,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal... | reasoning | {
"ground_truth": {
"entry": {
"answer": "84.29°",
"metadata": "{\"A\": [\"-4\", \"4\"], \"B\": [\"6\", \"5\"], \"C\": [\"6\", \"1\"], \"angle_ABC_degrees\": 84.28940686250036, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 11, \"t... | {
"index": 11,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(4, 7), B=(-1, 5), and C=(5, 2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(3.444, 5.889)",
"metadata": "{\"A\": [\"4\", \"7\"], \"B\": [\"-1\", \"5\"], \"C\": [\"5\", \"2\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"31/9\", \"53/9\"], \"orthocenter_approx\": [3.4444444444444446, 5.888888888888889], \"so... | {
"index": 12,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-4, -6), B=(-1, -8), and C=(-5, -1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2.... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-11.000, -10.000)",
"metadata": "{\"A\": [\"-4\", \"-6\"], \"B\": [\"-1\", \"-8\"], \"C\": [\"-5\", \"-1\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-11\", \"-10\"], \"orthocenter_approx\": [-11.0, -10.0], \"source_dataset\": \"... | {
"index": 13,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "8.06°",
"metadata": "{\"A\": [\"-10\", \"5\"], \"B\": [\"10\", \"6\"], \"C\": [\"-1\", \"7\"], \"angle_ABC_degrees\": 8.056834133846554, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 14, \... | {
"index": 14,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(1, 8), B=(9, -10), and C=(-3, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(0.273, 7.455)",
"metadata": "{\"A\": [\"1\", \"8\"], \"B\": [\"9\", \"-10\"], \"C\": [\"-3\", \"6\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"3/11\", \"82/11\"], \"orthocenter_approx\": [0.2727272727272727, 7.454545454545454], \... | {
"index": 15,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decima... | reasoning | {
"ground_truth": {
"entry": {
"answer": "75.96°",
"metadata": "{\"A\": [\"4\", \"2\"], \"B\": [\"1\", \"-1\"], \"C\": [\"-2\", \"4\"], \"angle_ABC_degrees\": 75.96375653207353, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 16, \"... | {
"index": 16,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-8, 10), B=(4, -10), and C=(-6, -1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2.... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-31.870, -16.522)",
"metadata": "{\"A\": [\"-8\", \"10\"], \"B\": [\"4\", \"-10\"], \"C\": [\"-6\", \"-1\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-733/23\", \"-380/23\"], \"orthocenter_approx\": [-31.869565217391305, -16.5217... | {
"index": 17,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-1, 8), B=(-6, -2), and C=(-3, 5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.223",
"metadata": "{\"A\": [\"-1\", \"8\"], \"B\": [\"-6\", \"-2\"], \"C\": [\"-3\", \"5\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.22319770263487862, \"incircle_radius_exact\": \"sqrt(-sqrt(13)/2 + sqrt(58)/2 ... | {
"index": 18,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-5, 7), B=(-4, 0), and C=(-1, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.158",
"metadata": "{\"A\": [\"-5\", \"7\"], \"B\": [\"-4\", \"0\"], \"C\": [\"-1\", \"0\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.1580887317290323, \"incircle_radius_exact\": \"sqrt(-3/2 + 5*sqrt(2)/2 + sqrt(6... | {
"index": 19,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. R... | reasoning | {
"ground_truth": {
"entry": {
"answer": "43.15°",
"metadata": "{\"A\": [\"-5\", \"-8\"], \"B\": [\"-3\", \"4\"], \"C\": [\"-1\", \"1\"], \"angle_ABC_degrees\": 43.1523897340054, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 20, \... | {
"index": 20,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(4, -1), B=(-2, 5), and C=(-8, 2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.959",
"metadata": "{\"A\": [\"4\", \"-1\"], \"B\": [\"-2\", \"5\"], \"C\": [\"-8\", \"2\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.959162194043828, \"incircle_radius_exact\": \"sqrt(-3*sqrt(17)/2 + 3*sqrt(5)/2 ... | {
"index": 21,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-7, 10), B=(9, 2), and C=(7, -10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Rou... | reasoning | {
"ground_truth": {
"entry": {
"answer": "3.819",
"metadata": "{\"A\": [\"-7\", \"10\"], \"B\": [\"9\", \"2\"], \"C\": [\"7\", \"-10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 3.818813450082334, \"incircle_radius_exact\": \"sqrt(-sqrt(149) + sqrt(37) + 4*s... | {
"index": 22,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-1, -1), B=(6, -3), and C=(4, 4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answe... | reasoning | {
"ground_truth": {
"entry": {
"answer": "2.080",
"metadata": "{\"A\": [\"-1\", \"-1\"], \"B\": [\"6\", \"-3\"], \"C\": [\"4\", \"4\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 2.080319990748767, \"incircle_radius_exact\": \"5*sqrt(2)*sqrt(-5*sqrt(2)/2 + sqr... | {
"index": 23,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-1, 3), B=(-3, 4), and C=(-1, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. R... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(2.000, 4.000)",
"metadata": "{\"A\": [\"-1\", \"3\"], \"B\": [\"-3\", \"4\"], \"C\": [\"-1\", \"-2\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"2\", \"4\"], \"orthocenter_approx\": [2.0, 4.0], \"source_dataset\": \"advanced_geome... | {
"index": 24,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-7, 3), B=(4, 3), and C=(-2, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-2.000, 8.000)",
"metadata": "{\"A\": [\"-7\", \"3\"], \"B\": [\"4\", \"3\"], \"C\": [\"-2\", \"9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-2\", \"8\"], \"orthocenter_approx\": [-2.0, 8.0], \"source_dataset\": \"advanced_geom... | {
"index": 25,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decima... | reasoning | {
"ground_truth": {
"entry": {
"answer": "23.40°",
"metadata": "{\"A\": [\"4\", \"6\"], \"B\": [\"-7\", \"9\"], \"C\": [\"8\", \"-3\"], \"angle_ABC_degrees\": 23.404689551032316, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 26, \... | {
"index": 26,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "133.23°",
"metadata": "{\"A\": [\"-9\", \"-7\"], \"B\": [\"-5\", \"-8\"], \"C\": [\"9\", \"1\"], \"angle_ABC_degrees\": 133.2285302599659, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 27,... | {
"index": 27,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-1, 4), B=(4, -6), and C=(0, -7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(1.556, -6.222)",
"metadata": "{\"A\": [\"-1\", \"4\"], \"B\": [\"4\", \"-6\"], \"C\": [\"0\", \"-7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"14/9\", \"-56/9\"], \"orthocenter_approx\": [1.5555555555555556, -6.222222222222222],... | {
"index": 28,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(6, 9), B=(-10, -2), and C=(-6, -4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal ans... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.828",
"metadata": "{\"A\": [\"6\", \"9\"], \"B\": [\"-10\", \"-2\"], \"C\": [\"-6\", \"-4\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.8277829342539866, \"incircle_radius_exact\": \"sqrt(-sqrt(313)/2 + sqrt(5) + ... | {
"index": 29,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, -5), B=(1, 7), and C=(9, 1), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2.... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(18.000, 7.000)",
"metadata": "{\"A\": [\"9\", \"-5\"], \"B\": [\"1\", \"7\"], \"C\": [\"9\", \"1\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"18\", \"7\"], \"orthocenter_approx\": [18.0, 7.0], \"source_dataset\": \"advanced_geome... | {
"index": 30,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-7, 6), B=(5, 8), and C=(-5, 4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answer... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.087",
"metadata": "{\"A\": [\"-7\", \"6\"], \"B\": [\"5\", \"8\"], \"C\": [\"-5\", \"4\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.0867758790164321, \"incircle_radius_exact\": \"sqrt(-sqrt(2) + sqrt(29) + sqrt(3... | {
"index": 31,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. R... | reasoning | {
"ground_truth": {
"entry": {
"answer": "116.57°",
"metadata": "{\"A\": [\"6\", \"-7\"], \"B\": [\"0\", \"-7\"], \"C\": [\"-1\", \"-5\"], \"angle_ABC_degrees\": 116.56505117707799, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 32... | {
"index": 32,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(8, 3), B=(4, -9), and C=(6, 5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.080",
"metadata": "{\"A\": [\"8\", \"3\"], \"B\": [\"4\", \"-9\"], \"C\": [\"6\", \"5\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.080363026950906, \"incircle_radius_exact\": \"sqrt(-2*sqrt(10) + 6*sqrt(2))*sqrt(... | {
"index": 33,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(4, 2), B=(-4, -1), and C=(-9, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.679",
"metadata": "{\"A\": [\"4\", \"2\"], \"B\": [\"-4\", \"-1\"], \"C\": [\"-9\", \"3\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.6794391712097267, \"incircle_radius_exact\": \"sqrt(-sqrt(170)/2 + sqrt(41)/2 +... | {
"index": 34,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(0, -4), B=(-3, -4), and C=(-7, -1). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal ans... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.576",
"metadata": "{\"A\": [\"0\", \"-4\"], \"B\": [\"-3\", \"-4\"], \"C\": [\"-7\", \"-1\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.5763403412041376, \"incircle_radius_exact\": \"sqrt(-1 + sqrt(58)/2)*sqrt(1 +... | {
"index": 35,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-7, -1), B=(-2, 3), and C=(-9, 10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-3.222, 2.778)",
"metadata": "{\"A\": [\"-7\", \"-1\"], \"B\": [\"-2\", \"3\"], \"C\": [\"-9\", \"10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-29/9\", \"25/9\"], \"orthocenter_approx\": [-3.2222222222222223, 2.777777777777777... | {
"index": 36,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(4, 1), B=(9, -5), and C=(-3, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(4.355, 3.129)",
"metadata": "{\"A\": [\"4\", \"1\"], \"B\": [\"9\", \"-5\"], \"C\": [\"-3\", \"-3\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"135/31\", \"97/31\"], \"orthocenter_approx\": [4.354838709677419, 3.129032258064516], ... | {
"index": 37,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(2, 7), B=(3, 1), and C=(1, 7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.448",
"metadata": "{\"A\": [\"2\", \"7\"], \"B\": [\"3\", \"1\"], \"C\": [\"1\", \"7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.44751680140974925, \"incircle_radius_exact\": \"sqrt(-1/2 + sqrt(37)/2 + sqrt(10))... | {
"index": 38,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round... | reasoning | {
"ground_truth": {
"entry": {
"answer": "45.00°",
"metadata": "{\"A\": [\"4\", \"0\"], \"B\": [\"7\", \"7\"], \"C\": [\"2\", \"5\"], \"angle_ABC_degrees\": 45.0, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 39, \"task_type\": \"... | {
"index": 39,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(5, 6), B=(-1, -5), and C=(-5, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. R... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-2.161, -3.548)",
"metadata": "{\"A\": [\"5\", \"6\"], \"B\": [\"-1\", \"-5\"], \"C\": [\"-5\", \"-2\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-67/31\", \"-110/31\"], \"orthocenter_approx\": [-2.161290322580645, -3.54838709677... | {
"index": 40,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(4, -8), B=(-6, 2), and C=(-9, -9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Rou... | reasoning | {
"ground_truth": {
"entry": {
"answer": "3.629",
"metadata": "{\"A\": [\"4\", \"-8\"], \"B\": [\"-6\", \"2\"], \"C\": [\"-9\", \"-9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 3.628607399910975, \"incircle_radius_exact\": \"sqrt(-sqrt(130)/2 + sqrt(170)/2 ... | {
"index": 41,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. R... | reasoning | {
"ground_truth": {
"entry": {
"answer": "86.25°",
"metadata": "{\"A\": [\"-1\", \"-9\"], \"B\": [\"5\", \"-10\"], \"C\": [\"6\", \"0\"], \"angle_ABC_degrees\": 86.24827092947403, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 42, ... | {
"index": 42,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, -7), B=(0, -4), and C=(-3, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-8.905, -13.714)",
"metadata": "{\"A\": [\"9\", \"-7\"], \"B\": [\"0\", \"-4\"], \"C\": [\"-3\", \"4\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-187/21\", \"-96/7\"], \"orthocenter_approx\": [-8.904761904761905, -13.71428571428... | {
"index": 43,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(7, 0), B=(-10, -8), and C=(6, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(13.371, -5.663)",
"metadata": "{\"A\": [\"7\", \"0\"], \"B\": [\"-10\", \"-8\"], \"C\": [\"6\", \"10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"1190/89\", \"-504/89\"], \"orthocenter_approx\": [13.370786516853933, -5.6629213483... | {
"index": 44,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-4, 7), B=(-7, -2), and C=(0, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-21.333, 17.111)",
"metadata": "{\"A\": [\"-4\", \"7\"], \"B\": [\"-7\", \"-2\"], \"C\": [\"0\", \"10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-64/3\", \"154/9\"], \"orthocenter_approx\": [-21.333333333333332, 17.111111111111... | {
"index": 45,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-4, 0), B=(-5, 10), and C=(-10, 6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "2.165",
"metadata": "{\"A\": [\"-4\", \"0\"], \"B\": [\"-5\", \"10\"], \"C\": [\"-10\", \"6\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 2.16534569868405, \"incircle_radius_exact\": \"sqrt(-sqrt(101)/2 + sqrt(41)/2 +... | {
"index": 46,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, -2), B=(-6, 1), and C=(-8, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-6.324, 2.378)",
"metadata": "{\"A\": [\"9\", \"-2\"], \"B\": [\"-6\", \"1\"], \"C\": [\"-8\", \"-6\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-234/37\", \"88/37\"], \"orthocenter_approx\": [-6.324324324324325, 2.37837837837837... | {
"index": 47,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-8, 5), B=(8, 8), and C=(-1, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-3.695, 24.373)",
"metadata": "{\"A\": [\"-8\", \"5\"], \"B\": [\"8\", \"8\"], \"C\": [\"-1\", \"10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-218/59\", \"1438/59\"], \"orthocenter_approx\": [-3.694915254237288, 24.37288135593... | {
"index": 48,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(8, -5), B=(-5, 2), and C=(4, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(5.416, 6.629)",
"metadata": "{\"A\": [\"8\", \"-5\"], \"B\": [\"-5\", \"2\"], \"C\": [\"4\", \"4\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"482/89\", \"590/89\"], \"orthocenter_approx\": [5.415730337078652, 6.629213483146067], ... | {
"index": 49,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(6, 8), B=(7, 7), and C=(8, -2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.387",
"metadata": "{\"A\": [\"6\", \"8\"], \"B\": [\"7\", \"7\"], \"C\": [\"8\", \"-2\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.3870785866001241, \"incircle_radius_exact\": \"sqrt(-sqrt(2)/2 + sqrt(82)/2 + sqr... | {
"index": 50,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(8, 1), B=(-7, -8), and C=(1, -6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.178",
"metadata": "{\"A\": [\"8\", \"1\"], \"B\": [\"-7\", \"-8\"], \"C\": [\"1\", \"-6\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.178498732647984, \"incircle_radius_exact\": \"sqrt(-sqrt(17) + 7*sqrt(2)/2 + 3*... | {
"index": 51,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round de... | reasoning | {
"ground_truth": {
"entry": {
"answer": "55.62°",
"metadata": "{\"A\": [\"-5\", \"-7\"], \"B\": [\"-2\", \"-1\"], \"C\": [\"3\", \"-10\"], \"angle_ABC_degrees\": 55.61965527615514, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 52... | {
"index": 52,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. R... | reasoning | {
"ground_truth": {
"entry": {
"answer": "119.45°",
"metadata": "{\"A\": [\"6\", \"7\"], \"B\": [\"-6\", \"5\"], \"C\": [\"-10\", \"-6\"], \"angle_ABC_degrees\": 119.44542872992561, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 53... | {
"index": 53,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(0, 2), B=(-4, -7), and C=(0, -9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.738",
"metadata": "{\"A\": [\"0\", \"2\"], \"B\": [\"-4\", \"-7\"], \"C\": [\"0\", \"-9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.7376885134372428, \"incircle_radius_exact\": \"sqrt(-11/2 + sqrt(5) + sqrt(97)/... | {
"index": 54,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(3, 1), B=(-9, 8), and C=(-10, 7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-7.421, 11.421)",
"metadata": "{\"A\": [\"3\", \"1\"], \"B\": [\"-9\", \"8\"], \"C\": [\"-10\", \"7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-141/19\", \"217/19\"], \"orthocenter_approx\": [-7.421052631578947, 11.421052631578... | {
"index": 55,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(8, -9), B=(1, 3), and C=(-9, 5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answer... | reasoning | {
"ground_truth": {
"entry": {
"answer": "2.299",
"metadata": "{\"A\": [\"8\", \"-9\"], \"B\": [\"1\", \"3\"], \"C\": [\"-9\", \"5\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 2.298691118922622, \"incircle_radius_exact\": \"sqrt(-sqrt(193)/2 + sqrt(26) + sqr... | {
"index": 56,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(2, -4), B=(9, -5), and C=(-3, -3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Rou... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.082",
"metadata": "{\"A\": [\"2\", \"-4\"], \"B\": [\"9\", \"-5\"], \"C\": [\"-3\", \"-3\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.08218408348524164, \"incircle_radius_exact\": \"sqrt(-5*sqrt(2)/2 + sqrt(26)/2... | {
"index": 57,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(4, 4), B=(-5, 2), and C=(1, 3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(13.667, -54.000)",
"metadata": "{\"A\": [\"4\", \"4\"], \"B\": [\"-5\", \"2\"], \"C\": [\"1\", \"3\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"41/3\", \"-54\"], \"orthocenter_approx\": [13.666666666666666, -54.0], \"source_datas... | {
"index": 58,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Rou... | reasoning | {
"ground_truth": {
"entry": {
"answer": "19.65°",
"metadata": "{\"A\": [\"-4\", \"7\"], \"B\": [\"1\", \"4\"], \"C\": [\"-9\", \"6\"], \"angle_ABC_degrees\": 19.653824058053306, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 59, \... | {
"index": 59,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, 1), B=(-5, 7), and C=(9, -5), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(14.143, 7.000)",
"metadata": "{\"A\": [\"9\", \"1\"], \"B\": [\"-5\", \"7\"], \"C\": [\"9\", \"-5\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"99/7\", \"7\"], \"orthocenter_approx\": [14.142857142857142, 7.0], \"source_dataset\":... | {
"index": 60,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "92.29°",
"metadata": "{\"A\": [\"4\", \"-4\"], \"B\": [\"-8\", \"9\"], \"C\": [\"-7\", \"10\"], \"angle_ABC_degrees\": 92.29061004263853, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 61, ... | {
"index": 61,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-10, -5), B=(-7, -6), and C=(-7, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-6.000, -5.000)",
"metadata": "{\"A\": [\"-10\", \"-5\"], \"B\": [\"-7\", \"-6\"], \"C\": [\"-7\", \"-8\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-6\", \"-5\"], \"orthocenter_approx\": [-6.0, -5.0], \"source_dataset\": \"advan... | {
"index": 62,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "3.41°",
"metadata": "{\"A\": [\"1\", \"8\"], \"B\": [\"-7\", \"-10\"], \"C\": [\"-1\", \"6\"], \"angle_ABC_degrees\": 3.406443754994719, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 63, \... | {
"index": 63,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decim... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.47°",
"metadata": "{\"A\": [\"5\", \"-10\"], \"B\": [\"7\", \"6\"], \"C\": [\"5\", \"-9\"], \"angle_ABC_degrees\": 0.46962701968964715, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 64, ... | {
"index": 64,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, 8), B=(3, 5), and C=(-1, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-11.778, 15.556)",
"metadata": "{\"A\": [\"9\", \"8\"], \"B\": [\"3\", \"5\"], \"C\": [\"-1\", \"-6\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-106/9\", \"140/9\"], \"orthocenter_approx\": [-11.777777777777779, 15.5555555555555... | {
"index": 65,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-8, 2), B=(-2, 2), and C=(-4, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-4.000, 1.200)",
"metadata": "{\"A\": [\"-8\", \"2\"], \"B\": [\"-2\", \"2\"], \"C\": [\"-4\", \"-8\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-4\", \"6/5\"], \"orthocenter_approx\": [-4.0, 1.2], \"source_dataset\": \"advanced_... | {
"index": 66,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-3, 4), B=(4, 7), and C=(-9, -7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "1.503",
"metadata": "{\"A\": [\"-3\", \"4\"], \"B\": [\"4\", \"7\"], \"C\": [\"-9\", \"-7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 1.5031575084634152, \"incircle_radius_exact\": \"sqrt(-sqrt(157)/2 + sqrt(58)/2 +... | {
"index": 67,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(9, -3), B=(3, 5), and C=(-2, 10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.293",
"metadata": "{\"A\": [\"9\", \"-3\"], \"B\": [\"3\", \"5\"], \"C\": [\"-2\", \"10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.2932512261526581, \"incircle_radius_exact\": \"sqrt(-5 + 5*sqrt(2)/2 + sqrt(290... | {
"index": 68,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(0, 5), B=(-4, 2), and C=(3, 9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Roun... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(24.000, -19.000)",
"metadata": "{\"A\": [\"0\", \"5\"], \"B\": [\"-4\", \"2\"], \"C\": [\"3\", \"9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"24\", \"-19\"], \"orthocenter_approx\": [24.0, -19.0], \"source_dataset\": \"advanced... | {
"index": 69,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(8, 9), B=(-1, 4), and C=(3, -5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answer... | reasoning | {
"ground_truth": {
"entry": {
"answer": "2.885",
"metadata": "{\"A\": [\"8\", \"9\"], \"B\": [\"-1\", \"4\"], \"C\": [\"3\", \"-5\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 2.8848441598346626, \"incircle_radius_exact\": \"sqrt(-sqrt(106)/2 + sqrt(97)/2 + ... | {
"index": 70,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(10, -2), B=(-10, 5), and C=(7, 1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. R... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(18.308, 33.308)",
"metadata": "{\"A\": [\"10\", \"-2\"], \"B\": [\"-10\", \"5\"], \"C\": [\"7\", \"1\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"238/13\", \"433/13\"], \"orthocenter_approx\": [18.307692307692307, 33.307692307692... | {
"index": 71,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(8, -7), B=(0, -3), and C=(10, 9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(3.765, -3.471)",
"metadata": "{\"A\": [\"8\", \"-7\"], \"B\": [\"0\", \"-3\"], \"C\": [\"10\", \"9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"64/17\", \"-59/17\"], \"orthocenter_approx\": [3.764705882352941, -3.4705882352941178... | {
"index": 72,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-4, -7), B=(7, -7), and C=(0, 7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answe... | reasoning | {
"ground_truth": {
"entry": {
"answer": "3.737",
"metadata": "{\"A\": [\"-4\", \"-7\"], \"B\": [\"7\", \"-7\"], \"C\": [\"0\", \"7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 3.7367126240901958, \"incircle_radius_exact\": \"sqrt(-11/2 + sqrt(53) + 7*sqrt(5... | {
"index": 73,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "44.28°",
"metadata": "{\"A\": [\"9\", \"7\"], \"B\": [\"-1\", \"-10\"], \"C\": [\"10\", \"-7\"], \"angle_ABC_degrees\": 44.27933637748235, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 74,... | {
"index": 74,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-5, -5), B=(-4, 2), and C=(-5, 7), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(30.000, 2.000)",
"metadata": "{\"A\": [\"-5\", \"-5\"], \"B\": [\"-4\", \"2\"], \"C\": [\"-5\", \"7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"30\", \"2\"], \"orthocenter_approx\": [30.0, 2.0], \"source_dataset\": \"advanced_ge... | {
"index": 75,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "61.26°",
"metadata": "{\"A\": [\"10\", \"-5\"], \"B\": [\"-1\", \"-7\"], \"C\": [\"1\", \"-1\"], \"angle_ABC_degrees\": 61.26020470831195, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 76,... | {
"index": 76,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(-5, 7), B=(7, 3), and C=(-7, -8). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answe... | reasoning | {
"ground_truth": {
"entry": {
"answer": "4.124",
"metadata": "{\"A\": [\"-5\", \"7\"], \"B\": [\"7\", \"3\"], \"C\": [\"-7\", \"-8\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 4.124041480096933, \"incircle_radius_exact\": \"sqrt(-2*sqrt(10) + sqrt(229)/2 + ... | {
"index": 77,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "26.73°",
"metadata": "{\"A\": [\"-3\", \"-4\"], \"B\": [\"10\", \"8\"], \"C\": [\"4\", \"-8\"], \"angle_ABC_degrees\": 26.734564823055067, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 78,... | {
"index": 78,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-4, 8), B=(2, 10), and C=(-5, 9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-3.500, 4.500)",
"metadata": "{\"A\": [\"-4\", \"8\"], \"B\": [\"2\", \"10\"], \"C\": [\"-5\", \"9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-7/2\", \"9/2\"], \"orthocenter_approx\": [-3.5, 4.5], \"source_dataset\": \"advanced... | {
"index": 79,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "31.81°",
"metadata": "{\"A\": [\"-4\", \"9\"], \"B\": [\"-1\", \"-8\"], \"C\": [\"1\", \"-3\"], \"angle_ABC_degrees\": 31.80938928779315, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 80, ... | {
"index": 80,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-2, -8), B=(3, -2), and C=(-7, -9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(6.680, -20.400)",
"metadata": "{\"A\": [\"-2\", \"-8\"], \"B\": [\"3\", \"-2\"], \"C\": [\"-7\", \"-9\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"167/25\", \"-102/5\"], \"orthocenter_approx\": [6.68, -20.4], \"source_dataset\": ... | {
"index": 81,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(7, -10), B=(-5, -9), and C=(3, -2). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal ans... | reasoning | {
"ground_truth": {
"entry": {
"answer": "2.910",
"metadata": "{\"A\": [\"7\", \"-10\"], \"B\": [\"-5\", \"-9\"], \"C\": [\"3\", \"-2\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 2.9099178961149113, \"incircle_radius_exact\": \"sqrt(-sqrt(113)/2 + 2*sqrt(5) ... | {
"index": 82,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-3, 9), B=(-1, 8), and C=(-5, 1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-1.444, 8.111)",
"metadata": "{\"A\": [\"-3\", \"9\"], \"B\": [\"-1\", \"8\"], \"C\": [\"-5\", \"1\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-13/9\", \"73/9\"], \"orthocenter_approx\": [-1.4444444444444444, 8.11111111111111], ... | {
"index": 83,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "14.04°",
"metadata": "{\"A\": [\"-9\", \"8\"], \"B\": [\"9\", \"4\"], \"C\": [\"-3\", \"10\"], \"angle_ABC_degrees\": 14.036243467926477, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 84, ... | {
"index": 84,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, 8), B=(8, -7), and C=(-10, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(12.247, -11.483)",
"metadata": "{\"A\": [\"9\", \"8\"], \"B\": [\"8\", \"-7\"], \"C\": [\"-10\", \"-10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"1090/89\", \"-1022/89\"], \"orthocenter_approx\": [12.247191011235955, -11.483146... | {
"index": 85,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(2, 6), B=(1, -6), and C=(5, -10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-12.538, -8.538)",
"metadata": "{\"A\": [\"2\", \"6\"], \"B\": [\"1\", \"-6\"], \"C\": [\"5\", \"-10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-163/13\", \"-111/13\"], \"orthocenter_approx\": [-12.538461538461538, -8.538461538... | {
"index": 86,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.19°",
"metadata": "{\"A\": [\"6\", \"-2\"], \"B\": [\"-9\", \"2\"], \"C\": [\"10\", \"-3\"], \"angle_ABC_degrees\": 0.1878543416668164, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 87, ... | {
"index": 87,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round deci... | reasoning | {
"ground_truth": {
"entry": {
"answer": "4.76°",
"metadata": "{\"A\": [\"3\", \"-2\"], \"B\": [\"4\", \"10\"], \"C\": [\"4\", \"-10\"], \"angle_ABC_degrees\": 4.763641690726178, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 88, \... | {
"index": 88,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(1, 6), B=(-8, 2), and C=(-1, -10). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answ... | reasoning | {
"ground_truth": {
"entry": {
"answer": "3.411",
"metadata": "{\"A\": [\"1\", \"6\"], \"B\": [\"-8\", \"2\"], \"C\": [\"-1\", \"-10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 3.4114439199387214, \"incircle_radius_exact\": \"sqrt(-sqrt(193)/2 + sqrt(97)/2 ... | {
"index": 89,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(-6, 3), B=(-9, -5), and C=(-9, -1). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.684",
"metadata": "{\"A\": [\"-6\", \"3\"], \"B\": [\"-9\", \"-5\"], \"C\": [\"-9\", \"-1\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.6839943820237032, \"incircle_radius_exact\": \"sqrt(-1/2 + sqrt(73)/2)*sqrt(1... | {
"index": 90,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nConsider triangle ABC with coordinates A=(1, 5), B=(0, 9), and C=(0, 7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round d... | reasoning | {
"ground_truth": {
"entry": {
"answer": "0.239",
"metadata": "{\"A\": [\"1\", \"5\"], \"B\": [\"0\", \"9\"], \"C\": [\"0\", \"7\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 0.23925810073547518, \"incircle_radius_exact\": \"sqrt(-1 + sqrt(5)/2 + sqrt(17)/2)*... | {
"index": 91,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFind the incircle radius of triangle ABC whose vertices are A=(6, -4), B=(7, 10), and C=(-6, -10). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal ans... | reasoning | {
"ground_truth": {
"entry": {
"answer": "3.158",
"metadata": "{\"A\": [\"6\", \"-4\"], \"B\": [\"7\", \"10\"], \"C\": [\"-6\", \"-10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"incircle_radius_approx\": 3.1575378921983988, \"incircle_radius_exact\": \"sqrt(-sqrt(197)/2 + 3*sqrt(5) ... | {
"index": 92,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decim... | reasoning | {
"ground_truth": {
"entry": {
"answer": "26.57°",
"metadata": "{\"A\": [\"1\", \"10\"], \"B\": [\"10\", \"8\"], \"C\": [\"-2\", \"5\"], \"angle_ABC_degrees\": 26.56505117707799, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 93, \... | {
"index": 93,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decima... | reasoning | {
"ground_truth": {
"entry": {
"answer": "40.60°",
"metadata": "{\"A\": [\"3\", \"6\"], \"B\": [\"-9\", \"3\"], \"C\": [\"5\", \"-4\"], \"angle_ABC_degrees\": 40.60129464500447, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 94, \"... | {
"index": 94,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(-5, 3), B=(0, -4), and C=(-3, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-6.500, 2.500)",
"metadata": "{\"A\": [\"-5\", \"3\"], \"B\": [\"0\", \"-4\"], \"C\": [\"-3\", \"5\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-13/2\", \"5/2\"], \"orthocenter_approx\": [-6.5, 2.5], \"source_dataset\": \"advance... | {
"index": 95,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(2, 4), B=(-1, -4), and C=(6, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(3.440, -1.040)",
"metadata": "{\"A\": [\"2\", \"4\"], \"B\": [\"-1\", \"-4\"], \"C\": [\"6\", \"-2\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"86/25\", \"-26/25\"], \"orthocenter_approx\": [3.44, -1.04], \"source_dataset\": \"ad... | {
"index": 96,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nFor triangle with vertices A=(9, 7), B=(9, -1), and C=(7, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(85.500, -10.000)",
"metadata": "{\"A\": [\"9\", \"7\"], \"B\": [\"9\", \"-1\"], \"C\": [\"7\", \"-10\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"171/2\", \"-10\"], \"orthocenter_approx\": [85.5, -10.0], \"source_dataset\": \"adv... | {
"index": 97,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then answer.<|im_end|>\n<|im_start|>user\nGiven triangle ABC with coordinates A=(-10, -2), B=(-10, 7), and C=(-9, -3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2... | reasoning | {
"ground_truth": {
"entry": {
"answer": "(-20.000, -3.000)",
"metadata": "{\"A\": [\"-10\", \"-2\"], \"B\": [\"-10\", \"7\"], \"C\": [\"-9\", \"-3\"], \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"ortho\": [\"-20\", \"-3\"], \"orthocenter_approx\": [-20.0, -3.0], \"source_dataset\": \"ad... | {
"index": 98,
"source_dataset": "advanced_geometry",
"split": "train"
} |
reasoning_gym | [
{
"content": "<|im_start|>system\nYou are a helpful assistant. Think step by step, then 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. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Ro... | reasoning | {
"ground_truth": {
"entry": {
"answer": "67.52°",
"metadata": "{\"A\": [\"-10\", \"8\"], \"B\": [\"5\", \"-5\"], \"C\": [\"8\", \"4\"], \"angle_ABC_degrees\": 67.5205656028969, \"difficulty\": {\"max_coord\": 10, \"min_coord\": -10}, \"source_dataset\": \"advanced_geometry\", \"source_index\": 99, \"... | {
"index": 99,
"source_dataset": "advanced_geometry",
"split": "train"
} |
End of preview. Expand in Data Studio
RLVR generated dataset
Procedural rows from reasoning-gym, formatted for verl GRPO.
Build metadata
{
"config": "/home/owais/Projects/rlvr/rlvr/configs/datasets/advanced_geometry-instruct.yaml",
"template_type": "qwen-instruct",
"developer_prompt": null,
"data_source": "reasoning_gym",
"default_extract": "answer_tag",
"train_rows": 100000,
"test_rows": 4096,
"train_seed": 42,
"test_seed": 43,
"tasks": {
"advanced_geometry": {
"weight": 1,
"config": {}
}
},
"reasoning_gym_version": "0.1.19"
}
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