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) geometrycircumcirclecyclic quadrilateralradical axisgeometry proposedAngle Chasing