It is given triangle $ABC$. Let internal and external angle bisector of angle $\angle BAC$ intersect line $BC$ in points $D$ and $E$, respectively, and circumcircle of triangle $ADE$ intersects line $AC$ in point $F$. Prove that $FD$ is angle bisector of $\angle BFC$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017
Tags: geometry, angle bisector, circumcircle