Question 189
Let $\triangle ABC$ be acute triangle. Point $M$ is arbitrary point on the side $AB$, and $N$ is the midpoint of $AC$. Denote by $P$ and $Q$ the feet of the perpendiculars from $A$ to the lines $MC$ and $MN$, respectively. Prove that when $M$ vary then the circumcenter of $\triangle PQN$ lies on a fixed line.