Question #N219

A circle with center (2, -3) passes through the point (5, 0). What is the radius of the circle?
A. 2
B. 3
C. 5
D. 8

Correct Answer is: C

The radius of a circle is the distance from the center of the circle to any point on the circle. We can use the distance formula to find the distance between the center (2, -3) and the point (5, 0). The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. Plugging in the values, we get $\sqrt{(5-2)^2 + (0-(-3))^2} = \sqrt{3^2 + 3^2} = \sqrt{18} = 3\sqrt{2}$. Since the distance is $3\sqrt{2}$, the radius is $3\sqrt{2}$, and the square of the radius is $(3\sqrt{2})^2 = 18$. Therefore, the radius is $\sqrt{18} = 3\sqrt{2}$.