RMO 2025 Problem 5

Let $ABC$ be an acute-angled triangle with $AB<AC$ , orthocenter $H$ and circumcircle $\Omega$ . Let $M$ be the midpoint of the minor arc $BC$ of $\Omega$ . Suppose the $MH$ is equal to the radius of $\Omega$ . Prove that $\angle BAC=60^\circ$ Proposed by Rijul Saini