UPSC CSE Prelims 2020
Consider the following statements:
- The minimum number of points of intersection of a square and a circle is 2.
- The maximum number of points of intersection of a square and a circle is 8.
Which of the above statements is/are correct?
EXPLANATION
Correct Option (B)
Statement 2 is correct. A circle can intersect each side of a square at a maximum of two distinct points. Since a square possesses four sides, the theoretical maximum number of intersection points between a square and a circle is 4 sides multiplied by 2 points per side, resulting in 8 points. This configuration is geometrically achievable.
Incorrect Options:
Statement 1 is incorrect. The minimum number of points of intersection between a square and a circle is 0. This occurs when the square and the circle are positioned such that their boundaries do not touch or overlap at any point. For example, one shape can be entirely contained within the other without contact, or they can be completely separate entities. Therefore, the assertion that the minimum number of intersection points is 2 is factually incorrect.
