messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-10, 2), B=(-5, -2), and C=(-10, 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 rad... | 1.373 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, -1), B=(6, 6), and C=(7, -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... | 1.642 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, 1), B=(-8, -1), 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... | (-1.000, 6.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, -10), B=(7, -2), 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, ... | (-47.000, 1.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 6), B=(-9, 0), and C=(7, 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, coordinat... | 2.172 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 3), B=(-3, -6), and C=(-6, -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, ... | 90.00° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -9), B=(-10, 1), and C=(-7, -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 radi... | 0.352 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, -7), B=(-1, -6), and C=(-2, 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... | 0.833 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, -6), B=(4, -9), 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... | (14.222, -6.444) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 6), B=(-2, 6), 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 ... | 0.230 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 1), B=(-3, 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... | 1.479 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, -2), B=(5, 1), and C=(0, 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, coordinat... | 1.078 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, 2), B=(-7, 0), and C=(-9, 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 ... | 2.621 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, 0), B=(10, 4), and C=(6, 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, coordi... | 23.63° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, -7), B=(-1, 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 radi... | 0.840 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, 6), B=(4, 9), and C=(-6, -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... | 1.056 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(7, -6), B=(6, 5), 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, coordinat... | 0.892 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-4, 9), B=(6, -7), and C=(10, -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... | 65.70° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, 3), B=(1, -4), and C=(3, 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, coordi... | (1.000, 1.857) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, -8), B=(9, -8), and C=(-10, 8), 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, ... | 40.10° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 1), B=(-8, 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 radius... | 2.717 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, -1), B=(6, 0), and C=(-5, -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, ... | 19.25° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, -3), B=(-5, -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 decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates,... | 7.13° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, -6), B=(3, -1), 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 radi... | 1.014 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, 1), B=(3, -3), and C=(0, 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 radius ... | 1.516 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, 8), B=(5, -1), and C=(-1, 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... | 39.47° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, -1), B=(4, 1), and C=(-1, -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, coordin... | 0.688 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 8), B=(-4, 7), and C=(-2, -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, ... | (-3.291, 6.618) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(2, -1), B=(4, 3), 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | 145.30° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-2, 0), B=(3, 9), and C=(-3, 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, or... | 60.95° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 9), B=(-7, 9), 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 56.31° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(8, -1), B=(10, 0), and C=(-8, -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, coordi... | 0.328 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, -6), B=(3, 2), 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, coordinat... | 1.677 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, -6), B=(-6, -4), 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 radiu... | 3.923 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, -3), B=(-4, 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, coordi... | 1.536 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(8, -10), B=(-1, 9), 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, coor... | (-10.113, -12.264) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 8), B=(-3, 1), and C=(-2, -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... | 0.410 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -5), B=(-8, 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. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | 14.74° | Puzzle | advanced_geometry |
[
{
"content": "For 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)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (0.273, 7.455) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 4), B=(-10, -10), and C=(-5, 8), 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... | 3.43° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 2), B=(-2, 4), and C=(4, 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... | 0.513 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 8), B=(1, -10), and C=(7, -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, o... | 40.73° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-1, 10), B=(-9, 0), and C=(-10, -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... | 167.91° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, -9), B=(-10, 1), and C=(-7, -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 angl... | (-10.000, -10.800) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, -5), B=(3, -3), and C=(-10, 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, coor... | (39.000, 99.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, -4), B=(-10, -4), and C=(-4, 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... | (-4.000, 14.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -3), B=(-4, 4), and C=(10, 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, ... | 26.57° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 4), B=(-9, 1), and C=(4, 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, c... | (5.414, 3.402) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -8), B=(-8, -9), and C=(-9, 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,... | 83.09° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 10), B=(8, 7), and C=(-9, -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... | 3.974 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-7, -4), B=(10, -5), 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,... | (6.477, -0.890) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-9, -7), B=(-9, -9), 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, coord... | 0.876 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, -8), B=(3, 5), 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 decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 72.90° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, -6), B=(-5, -10), and C=(-4, 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, c... | 54.52° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, 9), B=(10, -2), 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 decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, ... | 54.52° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, -9), B=(6, -6), and C=(7, 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... | 1.295 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, -4), B=(4, 6), and C=(-6, -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 radius... | 3.407 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(0, 2), B=(-1, 8), and C=(-3, 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, c... | (4.091, 10.182) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, 3), B=(-5, 7), and C=(-8, 8), 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... | 176.50° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, 5), B=(-2, 6), and C=(0, 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, coordin... | 34.70° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, 4), B=(6, 8), 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 decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or... | 49.76° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 9), B=(0, 3), and C=(-6, 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... | (-12.692, -7.154) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -4), B=(-1, 7), and C=(6, -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... | 3.912 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, 10), B=(1, -5), and C=(-5, 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, ... | 2.73° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -8), B=(-9, -3), and C=(-7, 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, coo... | 102.29° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, -2), B=(-10, -1), and C=(2, -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 angl... | (1.578, -16.438) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(8, 6), B=(8, 0), and C=(0, 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, coordina... | (8.000, 6.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, -1), B=(6, -1), 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... | 29.05° | Puzzle | advanced_geometry |
[
{
"content": "Find 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 answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radiu... | 0.223 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(7, 1), B=(-3, 0), and C=(-7, -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, ... | (-9.111, 17.111) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, -6), B=(-4, 6), and C=(1, -8), 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... | 1.22° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, 4), B=(6, -1), and C=(-2, -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, coor... | (-2.204, -2.367) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, -2), B=(0, 10), and C=(0, 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, ... | (36.000, -2.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -7), B=(6, 3), and C=(3, -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... | 2.985 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, -3), B=(-5, -9), and C=(-4, 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, coordi... | 3.627 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-5, 3), B=(9, 0), and C=(-4, 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, coordina... | 0.381 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -7), B=(9, 10), and C=(-5, -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, coo... | (-14.305, 6.116) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, 8), B=(-3, 2), 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, c... | (-1.049, 2.390) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 10), B=(-7, -1), and C=(-7, 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, coor... | (-12.500, 10.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(9, 5), B=(-4, -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 decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, ... | 81.09° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 1), B=(-4, 10), 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, coordi... | 1.074 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 10), B=(-8, 10), and C=(-2, 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 radiu... | 2.485 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-4, 1), B=(2, 2), and C=(-6, 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... | 50.65° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -9), B=(-10, 0), and C=(9, 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... | 4.440 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 9), B=(-5, 3), and C=(2, -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 radius ... | 3.503 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-2, 6), B=(0, -1), and C=(3, 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... | 39.14° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, 4), B=(0, 4), 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, co... | (9.000, 5.125) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 6), B=(-2, 9), and C=(-10, -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... | 1.764 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 5), B=(10, 8), and C=(3, -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... | (2.510, -1.736) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -10), B=(-6, 1), 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, co... | (-0.571, 3.714) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -3), B=(-5, 7), and C=(-4, 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, coordin... | 0.995 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 8), B=(-3, 0), and C=(-8, -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,... | (-6.400, 0.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(10, -9), B=(7, -7), and C=(2, 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... | 150.26° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -4), B=(1, -7), and C=(10, 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, ... | 19.44° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -2), B=(-4, 8), and C=(-6, 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... | 0.128 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(0, 7), B=(-10, -2), and C=(-6, 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, coordi... | 1.221 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, -10), B=(10, -3), and C=(0, -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, co... | 14.51° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, -6), B=(-7, -1), and C=(-10, -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 ang... | (-7.222, -1.778) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, 8), B=(-1, -6), and C=(4, -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... | (12.400, -6.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, 4), B=(-6, 1), 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, coordi... | (-6.273, 4.000) | Puzzle | advanced_geometry |
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