Consider the following statements: 1. The minimum number of points of intersection of a square and a circle…
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?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
A circle can be drawn entirely inside or outside a square with no points of intersection, so the minimum is 0, not 2 — Statement 1 is incorrect. A circle can cross each of the four sides of a square at most twice, giving a maximum of $4 \times 2 = 8$ points of intersection — Statement 2 is correct. Hence only 2 is correct.