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|. $$\begin{array}{ccc}\frac{{\left|AC\right|}^n}{{\left|AB\right|}^n}=\frac{\left|C{D}_n\right|}{\left|B{D}_n\right|},\hfill & \frac{{\left|AB\right|}^n}{{\left|BC\right|}^n}=\frac{\left|A{E}_n\right|}{\left|C{E}_n\right|},\hfill & \frac{{\left|BC\right|}^n}{{\left|AC\right|}^n}=\frac{\left|B{F}_n\right|}{\left|A{F}_n\right|}.\end{array}$$ 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.