Question 3
Let $ABC$ be a triangle. Let $M,N$ be the points where the median and angle bisector at $A$, respectively, meet $BC$. Let $Q,P$ be the points where the perpendicular at $N$ to $NA$ meets $MA,BA$, respectively, and $O$ the point where the perpendicular at $P$ to $BA$ meets $AN$ produced. Prove that $QO\perp BC$.
