Floating Triangle

Geometry Level 5

Triangle ABC is a triangle with all integer sides and area where a=15, b=4, and c=13. Points X,Y,Z are placed on sides AB, BC, CB respectively Such that \(AX:XB=1:12, BY:YC=2:1, CZ:ZA=1:1\). Cevians AY, BZ intersect at P; BZ, CX intersect at Q; and CX, AZ intersect at R. The area of triangle PQR can be expressed as \(\frac{m}{n}\) where m,n are positive co-prime integers. Find m+n.


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