Question 90
Let $ABCD$ be a cyclic quadrilateral with the intersection of internal angle bisectors of $\angle ABC$ and $\angle ADC$ lying on the diagonal $AC$. Let $M$ be the midpoint of $AC$. The line parallel to $BC$ that passes through $D$ intersects the line $BM$ in $E$ and the circumcircle of $ABCD$ at $F$ where $F \neq D$. Prove that $BCEF$ is a parallelogram.
