<Qua-2024-747>, hint

Let M, Miquel point  of circumcircles of triangles ABC, PBQ, APE, ECQ

CEM are cyclic <CME=<CQE and  CDM are cyclic<CMD=<CBD

<CQE+CBE=<QED=<DME. Hence circumcircle of C=DME is tangent to PQ at E

Hence M=R PBQR are concyclic.