There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?
Answer & explanation
Answer: (a) 24
Eight equidistant points form 4 diameters. The angle in a semicircle is a right angle, so each diameter with any of the other 6 points gives a right-angled triangle: 4 × 6 = 24.
- With 8 equidistant points, each point has a point exactly opposite it, giving 8 ÷ 2 = 4 diameters.
- The angle in a semicircle is a right angle, so a diameter with any third point forms a right-angled triangle.
- Each diameter can pair with any of the other 6 points: 4 × 6 = 24 triangles.
Remember · Angle in a semicircle = 90°: count diameters × remaining points.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·