MathNet 1989 — Part 01 Question 41

$ABC$ is a triangle. Points $D$, $E$, $F$ are chosen on $BC$, $CA$, $AB$ such that $B$ is equidistant from $D$ and $F$, and $C$ is equidistant from $D$ and $E$. Show that the circumcenter of $AEF$ lies on the bisector of $EDF$.