|
Journal for Geometry and Graphics 25 (2021), No. 1, 053--059 Copyright Heldermann Verlag 2021 Quadrigon Geometry: Circumscribed Squares and Van Aubel Points Chris van Tienhoven Prinses Beatrixstraat 1, 3981 BG Bunnik, Netherlands van10hoven@live.nl Dario Pellegrinetti Kirchstr. 16, 64283 Darmstadt, Germany d.pellegrinetti@alumni.sssup.it After a brief introduction on the quadrigon formal definition and the Van Aubel configuration, we present the main and original result of this work. The theorem establishes a connection between the Van Aubel configuration of a given quadrigon and the squares circumscribing the quadrigon. In particular, it states that the centers of the circumscribed squares coincide with the Van Aubel points. The proof is developed synthetically. Two different solutions to the problem of circumscribing a square to a given quadrigon are then given. Finally, a curious self-evident corollary regarding the six-point circle and the circumscribed rectangles of the quadrigon is presented. Keywords: quadrigon, circumscribed squares, Van Aubel points, six-point circle. MSC: 51F20, 51G05, 51M04, 51M15 [ Fulltext-pdf (492 KB)] |