Question

A circle is inscribed in a square whose vertices have coordinates R(0, 4), S(6, 2), T(4, -4), and U(-2, -2). Find the equation of the circle. (x - 2)² + y² = 68 (x + 2)² + y² = 20 (x - 2)² + y² = 10

Answer 1

(x - 2)^2 + y^2 = 10.

Explanation:

We can find the center and radius of the circle by finding the length of a side and center of a diagonal.

Side RS: Distance between R and S =

= √(6-0)^2 + (4-2)^2

= √40.

This is the diameter of the circle so the radius is √40 / 2.

The center of the circle is the midpoint of the diagonal

= (0+4)/ 2 , (4 - 4) / 2 = (2, 0).

Equation of a circle is (x - a)^2 + (y - b)^2 = r^2

Here a = 2, b = 0 and r^2 = (√40)^2 / 2)^2

= (40/ 2) / 2 = 10.

The answer is (x - 2)^2 + y^2 = 10.