PUMaC 2012 Geometry B Problem 8

A cyclic quadrilateral A B C D has side lengths A B=3, B C=A D=5, and C D=8. What’s the radius of its circumcircle? Your answer can be written in the form a \sqrt{b} / c, where a, b, c are positive integers, a, c are relatively prime, and b is not divisible by the square of any prime. Find a+b+c.