MathDB

P2

Part of 2024 PErA

Problems(1)

Locus of pastanaga points

Source: PErA 2024/2

3/4/2024
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.
geometryrectangle