Problem

Source: Turkey National Mathematical Olympiad 2019 P4

Tags: geometry



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