Question 74
The bisector of the inner angle $\angle ACB$ in an acute triangle $ABC$ intersects the side $AB$ at $D$. The circumcircle of the triangle $ADC$ intersects the side $BC$ in two distinct points, $C$ and $E$. The line through $B$ parallel to the line $AE$ intersects the line $CD$ at $F$. Prove that $AFB$ is an isosceles triangle.