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 \(m+n\).

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