CH-SMO 2023 Problem 1

Let $ABC$ be an acute triangle with incenter $I$ . On its circumcircle, let $M_A$ , $M_B$ and $M_C$ be the midpoints of minor arcs $BC, CA$ and $AB$ , respectively. Prove that the reflection $M_A$ over the line $IM_B$ lies on the circumcircle of the triangle $IM_BM_C$ .