Question 76
Let $D$ and $E$ be points on the sides $AB$ and $AC$ of $\triangle ABC$ such that $DE \parallel BC$. The circumcircle $k$ of $\triangle ADE$ meets the segments $BE$ and $CD$ at points $M$ and $N$. The lines $AM$ and $AN$ meet $BC$ at points $P$ and $Q$ such that $BC = 2PQ$ and $P$ lies between $B$ and $Q$. Prove that the circle $k$, the line $BC$ and the bisector of $\angle BAC$ are concurrent.