Question 91
Let $ABC$ be a triangle with greatest side $BC$ and let $D$ and $E$ be internal points on $AB$ and $AC$, respectively, such that $|AD| = |AE|$. Let $F$ and $G$ be internal points on $BC$ such that $|BD| = |BG|$ and $|CF| = |CE|$. Prove that $D$, $E$, $F$ and $G$ are concyclic.