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Locus of pastanaga points

Source: PErA 2024/2

March 4, 2024
geometryrectangle

Problem Statement

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