<Tri-2023-2046>, hint

Lei O' be the circumcenter of triangle ABC, and M be the midpoint of arc BC.

Since O lies on AM and OM//OP, and O',O,Q are colinear 

<MO'Q=<POO'=<OPQ+<OQP, <OPQ=<OQP.

<MO'Q=2MAQ. Hence A,Q,O,P are concyclic, <PQO=<PAO=<QAO.