Problem

Source: PErA 2024/2

Tags: geometry, rectangle



Let $ABCD$ be a fixed convex quadrilateral. Say a point $K$ is pastanaga if there's a rectangle $PQRS$ centered at $K$ such that $A\in PQ, B\in QR, C\in RS, D\in SP$. Prove there exists a circle $\omega$ depending only on $ABCD$ that contains all pastanaga points.