Several observations about Maneeals - a peculiar system of lines

Naga Vijay Krishna Dasari, Jakub Kabat

Abstract


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|.

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

Mathematics Subject Classification (2010)


51M04; 51M15; 51A20

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