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.