Mongolian National Mathematical Olympiad

Let $\omega$ be the circumcircle of a scalene triangle $ABC$. The tangents to $\omega$ at $A$ and $C$ meet in $P$, and the line $BP$ intersects $\omega$ in $D$. Let $B{B}^{\prime }$ be a diameter of $\omega$. The exterior angle bisector of $\angle ABC$ and the lines $B^{\prime }A$ and $B^{\prime }C$ intersect in $A^{\prime }$ and $C^{\prime }$, respectively. Prove that $A^{\prime },B^{\prime },C^{\prime },D$ are cyclic.