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2022 SSMO Team Round Problems/Problem 1

Revision as of 13:05, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== In triangle <math>ABC</math>, circumcircle <math>\omega</math> is drawn. Let <math>I</math> be the incenter of <math>\triangle{ABC}</math>. Let <math>H_A</math> be...")
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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 $m+n.$

Solution

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