Geodesic
Several observations about Maneeals - a peculiar system of lines
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016)

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For an arbitrary triangle ABC and an integer n we define points Dn, En, Fn on the sides BC, CA, AB respectively, in such a manner that|AC|n|AB|n=|CDn||BDn|,|AB|n|BC|n=|AEn||CEn|,|BC|n|AC|n=|BFn||AFn|. | AC|^n | AB|^n = | CD_n || BD_n |, | AB|^n | BC|^n = | AE_n || CE_n |, | BC|^n | AC|^n = | BF_n || AF_n |.Cevians ADn, BEn, CFn are said to be the Maneeals of order n. In this paper we discuss some properties of the Maneeals and related objects.
Keywords: Maneeals, Maneeal’s Points, Maneeals triangle of order n, Maneeal’s Pedal triangle of order n, Cauchy-Schwarz inequality, Lemoine’s Pedal Triangle Theorem 
Dasari, Naga Vijay Krishna; Kabat, Jakub. Several observations about Maneeals - a peculiar system of lines. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016). http://geodesic.mathdoc.fr/item/AUPCM_2016_15_a8/
@article{AUPCM_2016_15_a8,
     author = {Dasari, Naga Vijay Krishna and Kabat, Jakub},
     title = {Several observations about {Maneeals} - a peculiar system of lines},
     journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
     year = {2016},
     number = {15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPCM_2016_15_a8/}
}
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