The points $(-3,2)$ and $(-2,3)$ lie on a circle whose center is on the $x$-axis. What is the radius of the circle?
I know that the distance from the center of the circle to any point on the circle is the radius, so I can use the distance formula to find the radius. Let $(h,0)$ be the center of the circle, where $h$ is some unknown value. Then the distance from $(h,0)$ to $(-3,2)$ is equal to the distance from $(h,0)$ to $(-2,3)$. Using the distance formula, I get that $(h+3)^2 + 2^2 = (h+2)^2 + 3^2$. Expanding the squares and simplifying, I get that $h^2 + 6h + 13 = h^2 + 4h + 13$, or $2h = 0$. So $h = 0$, and the center of the circle is at the origin. Now I can use either point to find the radius, since they are both the same distance from the origin. Using $(-3,2)$, I get that the radius is $\sqrt{(-3)^2 + 2^2} = \sqrt{13}$. 