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 circle is $8$. Which of the above statements is/are correct?

QUESTION

CSAT

Hard

Maths

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 circle is $8$ .

Which of the above statements is/are correct?

Select an option to attempt

Explanation

Considering statement 1: The minimum number of points of intersection between a square and a circle is 2. This can occur when the circle intersects two sides of the square. However, there is also a scenario where the square just touches the circle, resulting in only 1 point of intersection. Therefore, the minimum number of points of intersection of a square and a circle is 1, making statement 1 incorrect.

Considering statement 2: A circle can intersect a straight line at most 2 points, and since the square has 4 sides, the maximum number of points of intersection between the square and the circle is: $4 \times 2 = 8$ This is the maximum number of points of intersection, so statement 2 is correct.