2022 SSMO Team Round Problems/Problem 1

Problem

In triangle $ABC$ , circumcircle $\omega$ is drawn. Let $I$ be the incenter of $\triangle{ABC}$ . Let $H_A$ be the intersection of the $A$ -altitude and $\omega.$ Given that $AB=13,AC=15,$ and $BC=14,$ the area of triangle $AIH_A$ can be expressed as $\frac{m}{n},$ for relatively prime positive integers $m$ and $n.$ Find $m+n.$

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2022 SSMO Team Round Problems/Problem 1

Problem

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