Question 21
In a scalene triangle $ABC$ the interior bisector $BD$ is drawn, with $D$ on $AC$. Let $E$ and $F$, respectively, be the feet of the perpendiculars drawn from $A$ and $C$ towards the line $BD$, and let $M$ be the point on the side $BC$ such that $DM$ is perpendicular to $BC$. Prove that $\angle EMD = \angle DMF$.