Question 128
Let $ABC$ be a triangle with $AB \gt AC$, $AD$ its bisector, where $D$ is a point on the side $BC$, and $I$ its incenter. If $M$ is the midpoint of the segment $AD$ and $F$ is the point of intersection of the line $MB$ with the circumcircle of the triangle $BIC$, prove that: $AF \perp FC$.
(E. Psarras)
(E. Psarras)