COLLINEAR NPC CENTERS ?

Let ABC be a triangle, L a line passing through H (orthocenter), intersecting the sidelines BC,CA,AB at A',B',C', resp., La,Lb,Lc the reflections of L in the sidelines BC,CA,AB, resp. (concurrent at a point S on the circumcircle) and Ab,Ac the orthogonal projections of A' on Lb,Lc, resp., Bc,Ba the orthogonal projections of B' on Lc,La, resp. and Ca,Cb the orthogonal projections of C' on La,Lb, resp. The NPC centers Na,Nb,Nc of of A'AbAc, B'BcBa, C'CaCb resp. are collinear. (??)

Antreas P. Hatzipolakis, 30 Jan. 2013