Product of inradius and circumradius?

Geometry Level 4

We are given a triangle with a perimeter of 272 and the product of its sides equal to 314. If the product of its inradius and circumradius can be written as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

If you think no such triangle exists, type 1337 as your answer.