messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Given triangle ABC with coordinates A=(-4, 4), B=(-3, 6), and C=(5, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (-5.000, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, -5), B=(2, -7), and C=(-9, 7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | 30.04° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 7), B=(-5, -7), and C=(-1, -10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates... | 135.00° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, -6), B=(0, 8), and C=(1, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, c... | (9.400, -1.400) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 0), B=(9, -10), and C=(-7, 6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 2.834 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 1), B=(2, 4), and C=(-6, -4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (-7.286, 0.286) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, 9), B=(3, -2), and C=(-10, -6). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radiu... | 2.364 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 6), B=(-1, 0), and C=(-4, -10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, co... | (3.889, 1.833) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, -2), B=(6, -1), and C=(10, -10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates... | 109.20° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, 0), B=(8, 7), and C=(9, -1), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | 1.01° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 8), B=(4, 0), and C=(0, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, co... | (14.621, -4.828) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(6, -8), B=(-1, -8), and C=(9, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (9.000, -10.500) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 1), B=(-9, 5), and C=(7, 3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius a... | 1.265 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -2), B=(-7, 2), and C=(-7, -5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radi... | 2.008 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(2, -5), B=(0, 5), and C=(-7, 8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | (8.938, 11.188) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, -4), B=(6, -6), and C=(2, 3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or... | 44.24° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, -6), B=(0, -4), and C=(7, 8), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (-217.000, 120.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, -4), B=(-10, 5), and C=(-2, -3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coo... | (-15.500, -22.500) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, -1), B=(-10, 2), 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, c... | 18.43° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(8, 8), B=(2, 10), and C=(-1, 6), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | (1.333, 13.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, 3), B=(-4, 4), and C=(-9, 1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (-2.800, 1.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, -7), B=(-1, 10), and C=(6, 3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle,... | (7.889, 2.889) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, -8), B=(1, -1), and C=(6, 1). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius ... | 2.000 | Puzzle | advanced_geometry |
[
{
"content": "For 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)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle,... | (13.371, -5.663) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(2, -1), B=(-3, -3), and C=(1, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (4.189, -1.973) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -10), B=(0, 10), and C=(-8, -5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radi... | 4.365 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, -8), B=(-10, 9), and C=(7, 7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 45.88° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, 0), B=(8, -9), and C=(-2, -4), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | 15.42° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, -9), B=(4, -5), and C=(-7, -3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radi... | 2.137 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, 6), B=(-9, -8), and C=(-9, 0), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (-14.600, 6.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 5), B=(6, -7), and C=(-5, 8), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 13.63° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -5), B=(-4, -10), and C=(3, 4), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | 34.38° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, 6), B=(1, 2), and C=(-5, -3), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 66.37° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, 9), B=(-9, 4), and C=(1, -6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordina... | 3.547 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(9, 2), B=(-9, -9), and C=(-9, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (-7.778, 2.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, -5), B=(4, 8), and C=(-2, 2), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 10.30° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, 3), B=(7, 7), and C=(-5, -5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (-11.667, 11.667) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, -5), B=(-2, 1), and C=(-5, 9). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radiu... | 1.436 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 1), B=(-9, -1), and C=(-10, 7), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates,... | 75.32° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 0), B=(-1, 1), and C=(6, 6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordina... | 0.139 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -5), B=(7, -9), 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 decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, o... | 90.00° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 2), B=(-2, 1), and C=(4, 6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinat... | 0.853 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 8), B=(10, -3), and C=(5, 7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 2.385 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 3), B=(-4, 8), and C=(8, -1). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordina... | 0.693 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, -10), B=(9, 8), and C=(6, -8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | (12.327, -13.624) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, -3), B=(9, 4), and C=(1, 4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinat... | 2.286 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, 10), B=(-9, 1), and C=(-9, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle,... | (-22.500, 10.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -8), B=(4, -8), and C=(6, 10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | (6.000, -9.111) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, 4), B=(10, -7), and C=(-7, -10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coo... | (2.150, -2.514) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 8), B=(-8, -6), and C=(2, 1). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 3.533 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, -8), B=(-10, -8), and C=(3, 5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coo... | 45.00° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, 4), B=(-6, -9), and C=(0, -9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 2.366 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 10), B=(-2, -1), and C=(10, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle... | (-2.000, 17.636) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, 10), B=(1, 3), and C=(-2, 5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 0.925 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, -6), B=(0, -5), and C=(-10, 6). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radi... | 2.793 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -4), B=(7, -9), and C=(-5, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 0.979 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, 5), B=(-9, 3), and C=(-4, -2), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 54.46° | Puzzle | advanced_geometry |
[
{
"content": "Find 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 answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radi... | 2.910 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, -5), B=(-4, -3), and C=(-9, -4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, co... | (-3.727, -1.364) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, -2), B=(7, -5), and C=(-5, 9), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coo... | 39.39° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, 2), B=(2, 2), and C=(-9, 0), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, c... | (-9.000, 46.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-2, 5), B=(-3, 6), and C=(-6, 7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (1.000, 14.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, -5), B=(1, -1), and C=(-10, 2), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle,... | (10.000, 17.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 3), B=(-1, -1), and C=(-8, 2), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, o... | 127.06° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, 8), B=(-4, 6), and C=(-6, -7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 117.18° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, -4), B=(-9, -7), and C=(9, 9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 0.208 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, 2), B=(-8, -10), and C=(3, -7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radiu... | 2.427 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, -4), B=(1, 4), and C=(6, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle,... | (11.953, -3.302) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, 10), B=(-8, -10), and C=(1, 8). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radiu... | 0.393 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 2), B=(7, -6), and C=(8, -10). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radiu... | 1.217 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 0), B=(6, 4), and C=(-1, 2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | (3.364, -1.273) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-1, -8), B=(-3, -3), and C=(-8, -8). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | 1.799 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, 2), B=(-5, 6), and C=(-4, -5). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radiu... | 3.813 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, -8), B=(9, -7), and C=(-7, 3), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 58.57° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 4), B=(-5, 7), and C=(-5, -4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 2.382 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, 10), B=(7, 7), and C=(-1, -10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coo... | (2.344, 5.603) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, -3), B=(-7, -8), and C=(3, 0), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, o... | 19.01° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 7), B=(4, 6), and C=(-8, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (-8.450, -2.300) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 1), B=(-4, 0), and C=(8, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (6.569, 2.882) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, 7), B=(-2, 4), and C=(10, 0), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | (-0.091, 6.727) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, -8), B=(1, -7), and C=(-6, 3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (16.714, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-9, 2), B=(2, -6), and C=(4, 3), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, c... | (1.565, -0.348) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, -1), B=(6, 10), and C=(-7, 9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates,... | 30.11° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -7), B=(-10, -4), and C=(-10, 10). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or r... | 1.183 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 8), B=(1, -6), and C=(1, -10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 0.432 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, 4), B=(-4, 4), and C=(-1, 7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordina... | 1.387 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -8), B=(-5, 7), and C=(5, 9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | 3.491 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, 4), B=(5, 5), and C=(9, -4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinat... | 0.996 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, 5), B=(-4, -10), and C=(8, 0), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, o... | 11.53° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, 10), B=(-6, 3), and C=(-3, -5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | 99.70° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, -10), B=(7, 4), and C=(10, 8). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 1.345 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, 8), B=(-7, 6), and C=(-10, 10), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | 114.34° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, -4), B=(-8, -1), and C=(7, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | 2.619 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, -1), B=(0, 4), and C=(1, -6), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (3.158, -1.684) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 2), B=(7, -1), and C=(-3, 3). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | 1.497 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-8, -8), B=(-6, -5), and C=(2, -6), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates,... | 116.57° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-9, -1), B=(0, -10), and C=(-5, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, co... | (4.333, 7.333) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, 0), B=(-10, 1), and C=(8, 10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | 3.044 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, 8), B=(9, 0), and C=(7, 4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinate... | 0.212 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, 10), B=(1, 5), and C=(0, 5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | (-8.000, -9.400) | Puzzle | advanced_geometry |
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