
Journal for Geometry and Graphics 21 (2017), No. 1, 029035 Copyright Heldermann Verlag 2017 Addendum to Concurrency and Collinearity in Hexagons Nicolae Anghel Dept. of Mathematics, University of North Texas, Denton, TX 76203, U.S.A. anghel@unt.edu The author presented recently [J. Geometry Graphics 20 (2016) 161173] a remarkable trigonometric equation, tied to various possible concurrencies and collinearities associated to a hexagonal path. In this sequel we relate this equation to crossratios of collinear points, and consequently get a trigonometric form for Brianchon's theorem. We also show how limiting cases of our theorems yield new proofs for two classical theorems of Ceva and Menelaus. Keywords: Hexagon, crossratio, sinecross ratio theorem, Brianchon's theorem, Ceva's theorem, Menelaus' theorem. MSC: 51M04; 97G60, 51A05, 51A45 [ Fulltextpdf (299 KB)] 