I offer an old book in German on Triliner Coordinates.

Well ... it is available on-line, but it is an other thing to have in your

library the original copy and other thing to have an electronic copy :-)

Now about the conjecture:

A way to prove it is to find the locus of points with

the property in question.

That is:

Let ABC be a triangle and P a point.

Denote:

La, Lb, Lc = the Euler lines of PBC,PCA,PAB, resp.

Na, Nb, Nc = the NPC centers of PBC,PCA, PAB, resp.

The perpendicular to La at Na intersects BC,CA,AB at Aa, Ab,Ac,

resp.