ORTHOCENTERS

Let ABC be a triangle and A'B'C' the cevian triangle of P = I.

Denote:

Ab,Ac = the reflections of A' in BB', CC', resp.

Bc,Ba = the reflections of B' in CC', AA', resp.

Ca,Cb = the reflections of C' in AA', BB', resp.

Ha, Hb, Hc = the orthocenters of the triangles A'AbAc, B'BcCa, C'CaCb, resp.

H'a, H'b, H'c = the reflections of Ha, Hb, Hc in AA', BB', CC', resp.

Conjecture 1.:

The triangles ABC, HaHbHc are perspective.

Conjecture 2.:

The points H'a, H'b, H'c are collinear

Locus of variable P such that

1. ABC, HaHbHc are perspective

2. H'a, H'b, H'c are collinear?

Antreas P. Hatzipolakis, 17 May 2013