HYACINTHOS 25232

[Antreas P. Hatzipolakis]:

 

ORTHIC TRIANGLE VERSION

of Hyacinthos 25214

Let ABC be a triangle and A'B'C' the pedal triangle of H.

Denote:

Na, Nb, Nc = the NPC centers of HB'C', HC'A', HA'B', resp.

The circumcircles of AHNa, BHNb, CHNc are coaxial.

Second point of intersection?

 

[Peter Moses]:

Hi Antreas,

 

(2 a^4-3 a^2 b^2+b^4-3 a^2 c^2-2 b^2 c^2+c^4) (a^6-a^4 b^2-a^2 b^4+b^6-5 a^4 c^2-a^2 b^2 c^2-5 b^4 c^2+7 a^2 c^4+7 b^2 c^4-3 c^6) (a^6-5 a^4 b^2+7 a^2 b^4-3 b^6-a^4 c^2-a^2 b^2 c^2+7 b^4 c^2-a^2 c^4-5 b^2 c^4+c^6)::

on K025

isogonal conjugate of the inverse of X(1173) in the circumcircle.

 

Best regards,

Peter Moses.