Question 90
Let $\triangle ABC$ be an isosceles triangle ($AB = AC$) with incenter $I$. Circle $\omega$ passes through $C$ and $I$ and is tangent to $AI$. The circle $\omega$ intersects $AC$ and circumcircle of $\triangle ABC$ at $Q$ and $D$, respectively. Let $M$ be the midpoint of $AB$ and $N$ be the midpoint of $CQ$. Prove that $AD$, $MN$ and $BC$ are concurrent.