Question 84
Let $ABC$ be an acute triangle. Let $D$ be the foot of the angle bisector of $\angle BAC$ on $BC$. The line through $B$ perpendicular to $AD$ meets the circumcircle of $ADB$ again at $E$. Let $O$ be the circumcenter of $ABC$. Prove that $A$, $O$, and $E$ are collinear.