Nemotron-IMO-Bench 2026 G7

A quadrilateral $ABCD$ is divided into cyclic quadrilaterals $P_1,\ldots, P_n$ with pairwise disjoint interiors. We assume that no vertex of any $P_i$ is an interior point of a side of any $P_j$ or of a side of $ABCD$. Prove that $ABCD$ is a cyclic quadrilateral.