OSN 2020 Problem 1

Since this is already 3 PM (GMT +7) in Jakarta, might as well post the problem here.

Problem 1. Given an acute triangle $ABC$ and the point $D$ on segment $BC$ . Circle $c_1$ passes through $A, D$ and its centre lies on $AC$ . Whereas circle $c_2$ passes through $A, D$ and its centre lies on $AB$ . Let $P \neq A$ be the intersection of $c_1$ with $AB$ and $Q \neq A$ be the intersection of $c_2$ with $AC$ . Prove that $AD$ bisects $\angle{PDQ}$ .