TR-MO 2019 Problem 4

In a triangle $\Delta ABC$ , $|AB|=|AC|$ . Let $M$ be on the minor arc $AC$ of the circumcircle of $\Delta ABC$ different than $A$ and $C$ . Let $BM$ and $AC$ meet at $E$ and the bisector of $\angle BMC$ and $BC$ meet at $F$ such that $\angle AFB=\angle CFE$ . Prove that the triangle $\Delta ABC$ is equilateral.