1999 AIME Problems/Problem 14

Problem

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

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1999 AIME Problems/Problem 14

Problem

Solution

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