Question 19
Let $\omega$ be the circumcircle of a scalene triangle $ABC$. The tangents to $\omega$ at $A$ and $C$ meet at $P$, and the line $BP$ intersects $\omega$ at $D$. Let $BB'$ be a diameter of $\omega$. The exterior angle bisector of $\angle ABC$ intersects the lines $B'A$ and $B'C$ at $A'$ and $C'$, respectively. Prove that $A', B', C', D$ are concyclic.