CMO 2019 Problem 3

Let $O$ be the circumcenter of $\triangle ABC$ ( $AB<AC$ ), and $D$ be a point on the internal angle bisector of $\angle BAC$ . Point $E$ lies on $BC$ , satisfying $OE\parallel AD$ , $DE\perp BC$ . Point $K$ lies on $EB$ extended such that $EK=EA$ . The circumcircle of $\triangle ADK$ meets $BC$ at $P\neq K$ , and meets the circumcircle of $\triangle ABC$ at $Q\neq A$ . Prove that $PQ$ is tangent to the circumcircle of $\triangle ABC$ .