Question 81
Let $ABC$ be an acute triangle with incentre $I$. 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 of $M_{A}$ over the line $IM_{B}$ lies on the circumcircle of the triangle $IM_{B}M_{C}$.