Geodesic
Addendum to Concurrency and Collinearity in Hexagons
Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 29-35 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51M04, 97G60, 51A05, 51A45
Mots-clés : Hexagon, cross-ratio, sine-cross ratio theorem, Brianchon's theorem, Ceva's theorem, Menelaus' theorem 
@article{JGG_2017_21_1_JGG_2017_21_1_a2,
     author = {N. Anghel },
     title = {Addendum to {Concurrency} and {Collinearity} in {Hexagons}},
     journal = {Journal for geometry and graphics},
     pages = {29--35},
     year = {2017},
     volume = {21},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2017_21_1_JGG_2017_21_1_a2/}
}
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N. Anghel . Addendum to Concurrency and Collinearity in Hexagons. Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 29-35. http://geodesic.mathdoc.fr/item/JGG_2017_21_1_JGG_2017_21_1_a2/