HYACINTHOS 7876

 

Antreas P. Hatzipolakis

Dear Clark

Please add this point to ETC, whose we have
the homogeneous coordinates thanks to Barry:


[Antreas, rephrased]:

Let HaHbHc be the orthic triangle of ABC, and

Ab, Ac = the reflections of A in Hc, Hb, resp.
Bc, Ba = the reflections of B in Ha, Hc, resp.
Ca, Cb = the reflections of C in Hb, Ha, resp.

The Nine Point Circles of the triangles
AAbAc, BBcBa, CCaCb concur at a point
with:

[Barry Wolk]:

Barycentrics:

(sin 3A)(1 + cos 2B + cos 2C)/(cos A) : ... : ...

Antreas

PS: And the trilinears we get from the barycentrics
are trigonometrically simple:

((sin3A/sin2A) * (1 + cos2B + cos2C) ::)