Question 97
Let $\triangle ABC$ be an acute triangle with $|AB| \gt |AC|$. The internal angle bisector of $\angle BAC$ intersects $BC$ at $D$. Let $O$ be the circumcenter of $\triangle ABC$. Let $AO$ intersect the segment $BC$ at $E$. Let $J$ be the incenter of $\triangle AED$. Prove that if $\angle ADO = 45^\circ$ then $|OJ| = |JD|$.