MathNet 2016-part-02 — 184 problems (EN–VI) Question 151

Let $ABCD$ be a cyclic quadrilateral. Let lines $AD$ and $BC$ meet at $M$, and lines $AB$ and $CD$ meet at $N$. Let the line through $C$ parallel to $AB$ intersect the line $MN$ at $F$ and circumcircle of triangle $FND$ intersect the line $CF$ at $E$. Prove that $AE \parallel BC$.

(Proposed by Argilsan N.)