Question 6
Let $D$ be a point in the interior of an acute triangle $A B C$ such that $\angle B A D = \angle D B C$ and $\angle D A C = \angle B C D$. Let $P$ be a point on the circumcircle of triangle $A D B$. Assume that $P$ lies outside triangle $A B C$. A line through $P$ meets the ray $B A$ at $X$ and the ray $C A$ at $Y$ such that $\angle X P B = \angle P D B$. Show that $B Y$ and $C X$ intersect on $A D$.