Question 98
Let $ABCD$ be a convex quadrilateral such that $|AB| = |BC| = |CD|$. The lines $AB$ and $CD$ intersect at the point $E$, and the circumcircles of the triangles $ABC$ and $BDE$ intersect at $B$ and $F$. Let $P$ denote the intersection of the lines $AC$ and $BF$. Prove that $EP$ is the bisector of the angle $\angle AED$.