
Journal for Geometry and Graphics 24 (2020), No. 1, 049064 Copyright Heldermann Verlag 2020 Entangled: From Triangles to Polygons Konstantinos Myrianthis 58 Zan Moreas Street, Athens, P.C. 15231, Greece myrian@ath.forthnet.gr The aim of the present work is to study the configuration of two nsided 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 ngons, 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 [ Fulltextpdf (509 KB)] 