2025 SSMO Accuracy Round Problems/Problem 2

Problem

Let $ABC$ be a triangle with circumcircle $\omega$ . The midpoint of $AB$ is $M,$ and the line $CM$ intersects $\omega$ again at $P$ . Given $\angle BMC = 120^\circ,$ $\triangle BMC$ is isosceles, and $BC = 20,$ the length of $PM$ can be written as $\tfrac{a\sqrt{b}}{c},$ where $a,$ $b,$ and $c$ are positive integers such that $a$ and $c$ are relatively prime and $b$ is square-free. Find $a+b+c$ .

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2025 SSMO Accuracy Round Problems/Problem 2

Problem

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