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∈PQ,B∈QR,C∈RS,D∈SP. Prove there exists a circle ω depending only on ABCD that contains all pastanaga points.
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∈PQ,B∈QR,C∈RS,D∈SP. Prove there exists a circle ω depending only on ABCD that contains all pastanaga points.