HYACINTHOS 25026

[Antreas P. Hatzipolakis]:

 

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

Denote:

Ab, Ac = the orthogonal projections of A' on BH, CH, resp.

N1 = the NPC center of A'AbAc.

N12, N13 = the reflections of N1 in BH, CH, resp.

(Na) = the NPC of N1N12N13. Similarly (Nb), (Nc).

(Na), (Nb), (Nc) are concurrent.

[Peter Moses]:

Hi Antreas,

 

>(Na), (Nb), (Nc) are concurrent

(a^2+b^2-c^2) (a^2-b^2+c^2) (2 a^12-3 a^10 b^2-7 a^8 b^4+18 a^6 b^6-12 a^4 b^8+a^2 b^10+b^12-3 a^10 c^2+a^6 b^4 c^2+8 a^4 b^6 c^2-4 a^2 b^8 c^2-2 b^10 c^2-7 a^8 c^4+a^6 b^2 c^4-12 a^4 b^4 c^4+3 a^2 b^6 c^4-b^8 c^4+18 a^6 c^6+8 a^4 b^2 c^6+3 a^2 b^4 c^6+4 b^6 c^6-12 a^4 c^8-4 a^2 b^2 c^8-b^4 c^8+a^2 c^10-2 b^2 c^10+c^12)::
on lines {{4,10264},{25,10272},{30,9826 },{110,7715},{399,6995},{428, 1986},{1112,6756}},

Midpoint of X(1112) and X(6756).

3 X[428] + X[1986]

 

Best regards,

Peter Moses.