Question 24
Let $\triangle ABC$ be an acute-angled triangle such that $|AC| \gt |AB|$, and let $O$ be its circumcentre. The angle bisector of $\angle BAC$ meets the side $\overline{BC}$ at point $D$. The line through $B$ perpendicular to the line $AD$ intersects the line $AO$ at point $E$. Prove that points $A, B, D$ and $E$ all lie on the same circle.