Problem

Source: Bundeswettbewerb Mathematik 2024, Round 1 - Problem 3

Tags: geometry, circumcircle, geometry proposed, Angle Chasing, parallelogram



Let $ABCD$ be a parallelogram whose diagonals intersect in $M$. Suppose that the circumcircle of $ABM$ intersects the segment $AD$ in a point $E \ne A$ and that the circumcircle of $EMD$ intersects the segment $BE$ in a point $F \ne E$. Show that $\angle ACB=\angle DCF$.