Product of the Radii

Geometry Level 4

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

The circumradius and inradius of $\triangle ABC$ are $R$ and $r$ respectively.

If the quantity $R \times r$ can be written in the form $\dfrac{m}{n}$ , where $m$ and $n$ are coprime positive integers, find $m+n$ .