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2024 SSMO Team Round Problems/Problem 15

Revision as of 15:45, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== In triangle <math>ABC</math> inscribed in circle <math>\omega,</math> let <math>M</math> be the midpoint of <math>BC.</math> Denote <math>P</math> as the intersec...")
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Problem

In triangle $ABC$ inscribed in circle $\omega,$ let $M$ be the midpoint of $BC.$ Denote $P$ as the intersection of $AM$ with $\omega.$ If $BP = 9, CP = 13,$ and $AM = 20,$ find the perimeter of triangle $ABC.$

Solution

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