We are given a cyclic quadrilateral $ABCD$ with a point $E$ on the diagonal $AC$ such that $AD=AE$ and $CB=CE$. Let $M$ be the center of the circumcircle $k$ of the triangle $BDE$. The circle $k$ intersects the line $AC$ in the points $E$ and $F$. Prove that the lines $FM$, $AD$ and $BC$ meet at one point. (4th Middle European Mathematical Olympiad, Individual Competition, Problem 3)
Problem
Source:
Tags: geometry, circumcircle, cyclic quadrilateral, radical axis, geometry proposed, Angle Chasing