Incenters Are Important

Geometry Level 4

The internal bisectors of the angles of the \(\Delta ABC\) meet the sides \(BC, CA\) and \(AB\) at the points \(P, Q\) and \(R\) respectively. If \(AB= 13, BC=14,CA=15\), find the area of \(\triangle PQR\).

If this area can be expressed as \( \dfrac MN\), where \(M\) and \(N\) are coprime positive integers, find \(M+N\).

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