IT-CESENATICO 2020 Problem 4

Let $ABC$ be an acute-angled triangle with $AB=AC$ , let $D$ be the foot of perpendicular, of the point $C$ , to the line $AB$ and the point $M$ is the midpoint of $AC$ . Finally, the point $E$ is the second intersection of the line $BC$ and the circumcircle of $\triangle CDM$ . Prove that the lines $AE, BM$ and $CD$ are concurrents if and only if $CE=CM$ .