Baltic Way 2023 Shortlist

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