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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

Dario Pellegrinetti
Kirchstr. 16, 64283 Darmstadt, Germany

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

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