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Journal for Geometry and Graphics 24 (2020), No. 1, 049--064
Copyright Heldermann Verlag 2020

Entangled: From Triangles to Polygons

Konstantinos Myrianthis
58 Zan Moreas Street, Athens, P.C. 15231, Greece

The aim of the present work is to study the configuration of two n-sided polygons with cevians where the sides and cevians of the first polygon enclose a constant angle with respective cevians and sides of the second polygon. We prove the existence of such pairs of n-gons, where sides are exchanged with cevians, and we call these polygons "entangled". Among the findings, there are generalizations of Miquel's theorem and Simson lines.

Keywords: Orthologic triangles, entangled polygons, entanglement points, entanglement angle, Miquel point, Miquel circles, generalized Simson line.

MSC: 51M04

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