Question 145
In acute $\triangle ABC$, $BC \gt AB$. Let $D$ be the point on the side $AC$ such that $BD = BA$. Let $M$ be the midpoint of $BC$. The tangents at $D$ and $M$ to the circumcircle of $\triangle CDM$ intersect at point $E$. The line $BE$ intersects the side $AC$ at $F$. Prove that $A, B, M, F$ are concyclic.