OSN 2018 Problem 2

Let $\Gamma_1, \Gamma_2$ be circles that touch at a point $A$ , and $\Gamma_2$ is inside $\Gamma_1$ . Let $B$ be on $\Gamma_2$ , and let $AB$ intersect $\Gamma_1$ on $C$ . Let $D$ be on $\Gamma_1$ and $P$ be on the line $CD$ (may be outside of the segment $CD$ ). $BP$ intersects $\Gamma_2$ at $Q$ . Prove that $A,D,P,Q$ lie on a circle.