jmc

Since $A{B}^2+B{C}^2=A{C}^2$, triangle $ABC$ is a right triangle with right angle at $\angle B$. The circumcenter of a right triangle is the midpoint of the hypotenuse of the triangle. So, the midpoint of $\overline{AC}$ is the center of the circle, and the radius is $AC/2=\boxed{\frac{17}{2}}$.