Question

A circle is inscribed inside a square as shown. If graphed on the coordinate plane, the coordinates of the center of the circle would be (2, 5) and the coordinates of one other point on the circle would be (5,2). Find the perimeter of the square.

A) 12√2
B) 18
C) 24√2
D) 45

Answer 1

C) 24√2

Explanation:

The distance between the points is the radius of the circle. Use distance formula:

d² = (x₂ − x₁)² + (y₂ − y₁)²

d² = (5 − 2)² + (2 − 5)²

d² = 3² + 3²

d = 3√2

The radius of the circle is 3√2. The diameter of the circle is 6√2, so the side length of the square is 6√2. Therefore, the perimeter is 24√2.