ELMO SL 2018 G5

Let scalene triangle $ABC$ have altitudes $AD, BE, CF$ and circumcenter $O$ . The circumcircles of $\triangle ABC$ and $\triangle ADO$ meet at $P \ne A$ . The circumcircle of $\triangle ABC$ meets lines $PE$ at $X \ne P$ and $PF$ at $Y \ne P$ . Prove that $XY \parallel BC$ .

Proposed by Daniel Hu