MathNet 2022-part-02 — 197 problems (EN–VI) Question 4

Let $ABCD$ be a convex quadrilateral with $AB = BC = CD$ and $P$ its intersection of diagonals. Denote by $O_1, O_2$ the circumcenters of triangles $ABP, CDP$, respectively. Prove that $O_1BCO_2$ is a parallelogram.