Let $ABC$ an acute triangle and $D$ and $E$ the feet of heights by $A$ and $B$, respectively, and let $M$ be the midpoint of $AC$. The circle that passes through $D$ and $B$ and is tangent to $BE$ in $B$ intersects the line $BM$ in $F, F\neq B$. Show that $FM$ is the angle bisector of $\angle AFD$.