UPSC Prelims 2022 · CSAT
Question 56: Basic Numeracy
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?
AnswerUPSC’s answer is (a).
Eight equidistant points on a circle give 4 diameters. A triangle with a diameter as one side is right-angled at the third vertex (angle in a semicircle), whichever other point that is. Each diameter has 6 choices for the third point, so 4 × 6 = 24 triangles. No triangle is counted twice, as two diameters cannot both be sides of one triangle.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Correct: 4 diameters × 6 third points.
- (b) 16 assumes only 4 third points per diameter, but any of the other 6 works.
- (c) 12 assumes only 3 third points per diameter.
- (d) 8 assumes only 2 third points per diameter.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.