किसी वृत्त पर एक-समान दूरी वाले आठ बिन्दु हैं। इन बिन्दुओं को शीर्ष और व्यास को एक भुजा लेकर कितने समकोण त्रिभुज खींचे जा सकते हैं?
Read this question in English
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?
(a) 24 · (b) 16 · (c) 12 · (d) 8
उत्तर और व्याख्या · explanation in English
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). ·