Question 14
Point $P$ is located inside triangle $ABC$ so that angles $PAB,$ $PBC,$ and $PCA$ are all congruent. The sides of the triangle have lengths $AB = 13,$ $BC = 14,$ and $CA = 15,$ and the tangent of angle $PAB$ is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$