BALTIC-WAY 2023 Problem 12

Let $A B C$ be an acute triangle with $A B>A C$. The internal angle bisector of $\angle B A C$ intersects $B C$ at $D$. Let $O$ be the circumcentre of $A B C$. Let $A O$ intersect the segment $B C$ at $E$. Let $J$ be the incentre of $A E D$. Prove that if $\angle A D O=45^{\circ}$ then $O J=J D$.