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2023 WSMO Speed Round Problems/Problem 10

Revision as of 15:34, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Consider acute triangle <math>ABC</math>, <math>H</math> is the orthocenter. Extend <math>AH</math> to meet <math>BC</math> at <math>D</math>. The angle bisector...")
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Problem

Consider acute triangle $ABC$, $H$ is the orthocenter. Extend $AH$ to meet $BC$ at $D$. The angle bisector of $\angle{ABH}$ meets the midpoint of $AD$, $M$. If $AB=10, BH=4$, then the area of $ABC$ is $\frac{a\sqrt{b}}{c},$ for squarefree $b$ and relatively prime positive integers $a$ and $c.$ Find $a+b+c.$

Solution

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