Question 16
Let $ABC$ be an acute triangle and let $D$ be the foot of the altitude from $A$. The circle with centre $A$ passing through $D$ intersects the circumcircle of triangle $ABC$ in $X$ and $Y$, where the order of the points on this circumcircle is $A, X, B, C, Y$. Prove that $\angle B X D = \angle C Y D$.