HYACINTHOS 25650

[Antreas P. Hatzipolaks]:

Let ABC be a triangle.

Denote:

A', B', C' = the reflections of I in BC, CA, AB, resp.

H'  = the orthocenter of A'B'C'

The NPCs of AHH', BHH', CHH' are coaxial.

2nd intersection (other than the midpoint of HH')?

[Peter Moses]:

Hi Antreas,

 

(b-c)^2 (-a+b+c) (-a^2+b^2-b c+c^2) (-a^2 b+b^3-a^2 c+a b c-b^2 c-b c^2+c^3) (-a^4+2 a^3 b-2 a b^3+b^4+2 a^3 c-3 a^2 b c+2 a b^2 c+2 a b c^2-2 b^2 c^2-2 a c^3+c^4)::
on line {137,8286} and the NP Circle.

 

Best regards,

Peter Moses.