A Circular Circle

Geometry Level 3

A triangle ABC has side lengths AB, BC, CA equal to 13, 15, and 14 units respectively. A semicircle with center R is drawn inside the triangle such that the base of the circle is on the side BC and the semicircle is touching all the three sides of the triangle as shown in the figure.

The radius of this circle can be written in the form \(\large\frac{a}{b}\), where \(a\) and \(b\) are positive co-prime integers. Find the value of \(a+b\).

This question is taken from IMO 2nd level 2014.

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