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 ab\dfrac{a}{b}, where aa and bb are coprime positive integers, find a+ba+b.

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

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