Consider the following statements:
- 1.The minimum number of points of intersection of a square and a circle is 2.
- 2.The maximum number of points of intersection of a square and a circle is 8.
Which of the above statements is/are correct?
Answer & explanation
Answer: (b) 2 only
A circle and a square need not meet at all — a small circle can sit inside the square without touching it — so the minimum is 0, not 2. Each side is a straight segment that can cut a circle at most twice, so four sides give at most 8 points, and 8 is actually reachable.
- A small circle inside the square, or one far away from it, meets the square in 0 points — so the minimum is 0.
- A straight line meets a circle in at most 2 points; the square has 4 sides, so at most 4 × 2 = 8 points.
- 8 is reached by a circle with the square's centre whose radius is more than half the side but less than half the diagonal: it crosses each side twice.
- ✗ 1. The minimum is 0 — the circle can lie wholly inside or wholly outside the square without touching it.
- ✓ 2. Four sides × at most 2 crossings each = 8, and a suitably sized concentric circle achieves it.
Remember · For 'minimum' claims, look for the case where the figures do not touch at all; for 'maximum', count lines × 2 for a circle.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·