Product of the Radii

Geometry Level 4

For ABC\triangle ABC, the perimeter is 296\dfrac{29}{6} and the products of the three sides is 4.

The circumradius and inradius of ABC\triangle ABC are RR and rr respectively.

If the quantity R×rR \times r can be written in the form mn\dfrac{m}{n}, where mm and nn are coprime positive integers, find m+nm+n.

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