Journal for Geometry and Graphics 21 (2017), No. 1, 029--035
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) 161--173] a remarkable trigonometric equation, tied to various possible concurrencies and collinearities associated to a hexagonal path. In this sequel we relate this equation to cross-ratios 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, cross-ratio, sine-cross ratio theorem, Brianchon's theorem, Ceva's theorem, Menelaus' theorem.
MSC: 51M04; 97G60, 51A05, 51A45
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