1999 AIME Problem 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 m/n, where m_{} and n_{} are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.