Question 100
Let $ABC$ be a triangle. Let $AD$ be the angle bisector of the angle $\angle BAC$ and let $BE$ be the angle bisector of the angle $\angle ABC$, with $D$ interior to the side $BC$ and $E$ to the side $AC$. Let $M$ be a point interior to the side $BC$ such that $|CM| = |AE|$, and let $N$ be a point interior to the side $AC$ such that $|CN| = |BD|$. Show that the points $D, E, M$ and $N$ are all on a circle if and only if $|AB| = |AC|$.