Question 9
In a convex quadrilateral $ABCD$, let $E$ be the intersection of the diagonals. It is given that $\angle EDC = \angle DEC = \angle BAD$. If $F$ is a point on the line segment $[BC]$ such that $\angle BAF + \angle EBF = \angle BFE$, then show that $A, B, F, D$ are concyclic.