Question 70
Let $\triangle ABC$ be an acute-angled triangle with circumcircle $\omega$ and circumcentre $O$. Points $D \neq B$ and $E \neq C$ lie on $\omega$ such that $BD \perp AC$ and $CE \perp AB$. Let $CO$ meet $AB$ at $X$, and $BO$ meet $AC$ at $Y$. Prove that the circumcircles of triangles $\triangle BXD$ and $\triangle CYE$ have an intersection point on line $AO$.