messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 10), B=(7, -6), and C=(-8, -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... | 4.473 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -5), B=(-10, 1), 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, coo... | (-10.688, -7.938) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, -4), B=(-2, 1), and C=(3, 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, coordin... | 0.389 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 2), B=(-4, 7), and C=(7, -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, or... | 7.28° | Puzzle | advanced_geometry |
[
{
"content": "Consider 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 3.629 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -6), B=(-9, 6), and C=(5, 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, coordi... | 30.53° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, 0), B=(4, -10), 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, or... | 10.99° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 3), B=(7, 3), and C=(-4, -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, coordin... | 4.033 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, -3), B=(6, 3), and C=(-2, -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... | 58.17° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 3), B=(9, 10), and C=(-4, 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 ... | 2.299 | Puzzle | advanced_geometry |
[
{
"content": "Find 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 answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 3.737 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 3), B=(0, -8), and C=(0, 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 ... | 2.498 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-7, 9), B=(5, 5), and C=(8, 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... | (19.000, 35.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, -10), B=(-5, 1), and C=(4, 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, coord... | 62.12° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 8), B=(0, -9), and C=(-2, -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... | 0.929 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, -10), B=(-8, -6), and C=(-7, 5). 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... | 3.476 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -7), B=(4, -7), and C=(-1, -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 radi... | 0.807 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-8, 7), B=(1, -4), and C=(-1, 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... | 28.98° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, -3), B=(-10, 1), and C=(-7, 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 radi... | 2.059 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, 0), B=(-1, 1), and C=(-7, 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... | (-11.250, -19.500) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 3), B=(10, 8), and C=(-4, -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, coordi... | 4.416 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, -5), B=(9, -3), and C=(7, -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... | 1.310 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(1, 6), B=(7, -4), and C=(3, 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, coordin... | 12.53° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, 6), B=(-1, 5), 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, coordinat... | 1.136 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, 5), B=(-5, -5), 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... | 109.44° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, 10), B=(5, -1), and C=(7, -1), 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... | 114.44° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(8, 1), B=(-9, 7), and C=(3, -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, coordi... | 33.69° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, 6), B=(2, -5), and C=(5, -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, coord... | 105.26° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, -1), B=(-6, 2), and C=(-10, -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, coor... | 1.140 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 6), B=(-3, 0), and C=(2, 1), 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 ... | 22.38° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(8, -1), B=(0, 2), and C=(3, -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... | 52.74° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-6, 2), B=(1, 1), and C=(6, -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, coordi... | (10.500, 29.500) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 5), B=(7, 3), 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, coordi... | (-2.857, 6.286) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, -2), B=(-8, 6), and C=(4, 4), 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... | 20.28° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, 10), B=(4, -9), and C=(-5, -7), 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... | (-8.065, -8.290) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, -4), B=(-7, -3), and C=(4, 9), 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... | (1.895, -5.737) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, -9), B=(-4, 7), and C=(-5, 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... | 1.531 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-1, 4), B=(5, -5), 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, coordin... | 0.985 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-1, -3), B=(-10, -6), and C=(1, -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, co... | (-0.857, -1.429) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 7), B=(3, -8), and C=(-4, 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... | 10.67° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, -9), B=(-2, 3), and C=(5, -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... | (9.889, -0.963) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(10, -9), B=(-2, 5), 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, coor... | 12.30° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, 4), B=(6, -9), and C=(9, 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, coordi... | (-19.241, 7.828) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, -4), B=(-5, 0), and C=(-5, -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... | 0.919 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 2), B=(-9, 0), and C=(-5, 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, or... | 47.56° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-6, 1), B=(5, 7), and C=(9, 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, coordina... | 0.257 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -2), B=(3, -2), 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 radius... | 0.450 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, 10), B=(-8, -3), and C=(5, -2). 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... | 3.856 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, -9), B=(7, 2), and C=(-6, 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, coor... | 57.68° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 1), B=(10, -3), and C=(1, 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 ... | 0.794 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, 3), B=(-1, -4), and C=(-8, 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, coor... | 4.40° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 10), B=(-5, -8), and C=(9, 0), 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... | 63.43° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, 0), B=(-6, -8), and C=(9, -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,... | 77.04° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, -4), B=(6, 5), and C=(-4, -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... | (7.762, -4.693) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, -10), B=(10, -5), 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, ... | 2.73° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 1), B=(5, -3), and C=(-4, 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 ... | 2.084 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 10), B=(2, 5), 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, coordin... | 1.948 | Puzzle | advanced_geometry |
[
{
"content": "Given 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coo... | (-3.222, 2.778) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(1, -4), B=(-6, 2), and C=(-5, -1), 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,... | (-11.000, -8.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, -6), B=(8, 5), and C=(-2, 9), 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... | (5.174, 4.435) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, 8), B=(-1, -4), and C=(3, -2). 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... | 1.871 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 0), B=(3, -5), 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... | (4.421, -0.737) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 2), B=(5, 7), and C=(-3, -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 ... | 0.147 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-7, -8), B=(-5, 1), and C=(4, -5), 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,... | (-3.839, -3.258) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, -7), B=(1, -5), and C=(-2, -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, coor... | 1.464 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-6, -6), B=(-1, 8), and C=(5, 5), 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, ... | (0.333, 6.667) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, -9), B=(-1, -3), and C=(-1, 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 radi... | 2.818 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-2, -5), B=(10, 7), and C=(-7, -7), 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... | (30.667, -44.667) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, 7), B=(-6, 4), and C=(-4, 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... | 53.13° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-5, -4), B=(8, -7), 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,... | (8.000, -8.333) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, -8), B=(9, -7), and C=(5, 6), 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... | 162.90° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, -3), B=(3, -2), 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, coor... | (1.143, 7.286) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, -6), B=(-3, 4), and C=(8, -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, coordin... | 1.362 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -10), B=(3, -5), 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, ... | 156.37° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -5), B=(-9, 5), and C=(2, 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, coordi... | (1.853, 6.809) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, -4), B=(-10, -4), and C=(-10, 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... | 90.00° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, 0), B=(-2, -5), and C=(2, 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... | 1.711 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 8), B=(-7, -8), and C=(-5, 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, coor... | 8.95° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -6), B=(-4, 6), and C=(-4, -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, coordi... | 1.488 | Puzzle | advanced_geometry |
[
{
"content": "For 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, c... | (-11.778, 15.556) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, 6), B=(0, 6), and C=(-7, -5), 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,... | (-7.000, 4.091) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 4), B=(7, -10), and C=(4, 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... | 1.944 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, 5), B=(-2, 5), and C=(-4, -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... | 2.550 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(2, 10), B=(-2, -1), and C=(-1, -9), 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... | (-39.116, 4.860) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 10), B=(2, 6), and C=(-6, 5), 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... | 142.13° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, 5), B=(5, -5), and C=(7, -6), 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... | 116.57° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -9), B=(6, 7), and C=(10, -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, coordi... | 3.996 | Puzzle | advanced_geometry |
[
{
"content": "Given 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | (58.000, -130.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-6, 9), B=(0, -8), and C=(-5, 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, ... | (27.455, 19.455) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, -5), B=(4, 2), and C=(-8, -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 radiu... | 1.859 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 2), B=(-7, 3), and C=(5, 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 ... | 0.424 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-8, -7), B=(2, 6), 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 127.57° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 10), B=(2, -6), 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 decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, o... | 23.63° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -5), B=(7, -3), and C=(-10, -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, coo... | (3.027, -21.541) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 1), B=(-3, 3), and C=(5, -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, coordina... | 2.013 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, -4), B=(-10, 7), and C=(5, -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, ... | 7.19° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 1), B=(9, -9), and C=(10, -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, coordi... | 1.015 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -4), B=(5, -7), and C=(6, 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 ... | 2.196 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(8, -6), B=(-2, 4), and C=(8, -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... | (13.000, 4.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-2, -4), B=(-4, -4), and C=(6, -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, co... | 30.96° | Puzzle | advanced_geometry |
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