IGO 2022 A3

In triangle $ABC$ $(\angle A\neq 90^\circ)$ , let $O$ , $H$ be the circumcenter and the foot of the altitude from $A$ respectively. Suppose $M$ , $N$ are the midpoints of $BC$ , $AH$ respectively. Let $D$ be the intersection of $AO$ and $BC$ and let $H'$ be the reflection of $H$ about $M$ . Suppose that the circumcircle of $OH'D$ intersects the circumcircle of $BOC$ at $E$ . Prove that $NO$ and $AE$ are concurrent on the circumcircle of $BOC$ .

Proposed by Mehran Talaei