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?
- (a) 1 only
- (b) 2 only ✓ UPSC's answer
- (c) Both 1 and 2
- (d) Neither 1 nor 2
Why the answer is (b)
• Statement 1 is incorrect because a circle can be placed entirely inside a square without touching it, resulting in 0 points of intersection, which is less than 2.
• A square consists of 4 straight line segments (sides), and a circle is a single continuous curve.
• A straight line can intersect a circle at a maximum of 2 points.
• Since the square has 4 sides, the theoretical maximum number of intersection points is 4 sides × 2 points/side = 8 points.
• This maximum of 8 is achievable if the circle is large enough to cut through all four sides of the square twice.
• Therefore, only Statement 2 is correct, making option (b) the right answer.
Why the other options are wrong
- (a) 1 only
- Statement 1 is false because the minimum number of intersection points is 0, not 2.
- (c) Both 1 and 2
- Statement 1 is false because the minimum number of intersection points is 0, not 2.
- (d) Neither 1 nor 2
- Statement 2 is true because a square and a circle can intersect at a maximum of 8 points.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.