Question 41
Let $ABC$ be a scalene triangle. Let $N$ be the midpoint of arc $BAC$ of its circumcircle, and let $M$ be the midpoint of $BC$. Let $I_1,I_2$ be the incenters of $ABM,ACM$, respectively. Prove that $I_1,I_2,A,N$ are concyclic. (M. Kungozhin)