Several observations about Maneeals - a peculiar system of lines

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.