Question 175
Let $ABC$ be an acute triangle with $AB \lt AC$. Let $E$ and $F$ be the feet of the altitudes from $B$ and $C$, respectively, and let $M$ be the midpoint of $BC$. The tangent line to the circumcircle of $ABC$ at $A$ meets the line $BC$ at $P$. The line through $A$ parallel to the line $BC$ meets the line $EF$ at $Q$. Prove that the line $PQ$ is perpendicular to the line $AM$.