Question 6
We are given a cyclic quadrilateral $A B C D$ with a point $E$ on the diagonal $A C$ such that $A D = A E$ and $C B = C E$. Let $M$ be the center of the circumcircle $k$ of the triangle $B D E$. The circle $k$ intersects the line $A C$ in the points $E$ and $F$. Prove that the lines $F M$, $A D$, and $B C$ meet at one point.
