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.
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.