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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