Question 18
Let $ABC$ be an acute triangle with $AB \lt AC$. Let $D$, $E$, $F$ be the feet of the altitudes from $A$, $B$, $C$ respectively. The circumcircles of $AEF$ and $ABC$ meet again at $M$. Suppose the line $BM$ is tangent to the circumcircle of $AEF$. Prove that $M$, $F$, $D$ are collinear.