[Antreas P. Hatzipolakis]:
Let ABC be a triangle, A'B'C' the pedal triangle of H.
Denote:
Na, Nb, Nc = the reflections of N in HA', HB', HC', resp.
N1, N2, N3 = the NPC centers of NaB'C', NbC'A', NcA'B', resp.
A'B'C', N1N2N3 are orthologic.
The orthologic center (N1N2N3, A'B'C') is the NPC center of A'B'C'
Denote:
Na, Nb, Nc = the reflections of N in HA', HB', HC', resp.
N1, N2, N3 = the NPC centers of NaB'C', NbC'A', NcA'B', resp.
A'B'C', N1N2N3 are orthologic.
The orthologic center (N1N2N3, A'B'C') is the NPC center of A'B'C'
The other one (A'B'C', N1N2N3) ?
[Peter Moses]:
[Peter Moses]:
Hi Antreas,
>A'B'C', N1N2N3 are orthologic.
a^4 (a^2+b^2-c^2) (a^2-b^2-b c-c^2) (a^2-b^2+b c-c^2) (a^2-b^2+c^2) (a^12 b^4-6 a^10 b^6+15 a^8 b^8-20 a^6 b^10+15 a^4 b^12-6 a^2 b^14+b^16-a^10 b^4 c^2+10 a^6 b^8 c^2-20 a^4 b^10 c^2+15 a^2 b^12 c^2-4 b^14 c^2+a^12 c^4-a^10 b^2 c^4-2 a^8 b^4 c^4+9 a^4 b^8 c^4-11 a^2 b^10 c^4+4 b^12 c^4-6 a^10 c^6-4 a^4 b^6 c^6+2 a^2 b^8 c^6+4 b^10 c^6+15 a^8 c^8+10 a^6 b^2 c^8+9 a^4 b^4 c^8+2 a^2 b^6 c^8-10 b^8 c^8-20 a^6 c^10-20 a^4 b^2 c^10-11 a^2 b^4 c^10+4 b^6 c^10+15 a^4 c^12+15 a^2 b^2 c^12+4 b^4 c^12-6 a^2 c^14-4 b^2 c^14+c^16)::
a^4 (a^2+b^2-c^2) (a^2-b^2-b c-c^2) (a^2-b^2+b c-c^2) (a^2-b^2+c^2) (a^12 b^4-6 a^10 b^6+15 a^8 b^8-20 a^6 b^10+15 a^4 b^12-6 a^2 b^14+b^16-a^10 b^4 c^2+10 a^6 b^8 c^2-20 a^4 b^10 c^2+15 a^2 b^12 c^2-4 b^14 c^2+a^12 c^4-a^10 b^2 c^4-2 a^8 b^4 c^4+9 a^4 b^8 c^4-11 a^2 b^10 c^4+4 b^12 c^4-6 a^10 c^6-4 a^4 b^6 c^6+2 a^2 b^8 c^6+4 b^10 c^6+15 a^8 c^8+10 a^6 b^2 c^8+9 a^4 b^4 c^8+2 a^2 b^6 c^8-10 b^8 c^8-20 a^6 c^10-20 a^4 b^2 c^10-11 a^2 b^4 c^10+4 b^6 c^10+15 a^4 c^12+15 a^2 b^2 c^12+4 b^4 c^12-6 a^2 c^14-4 b^2 c^14+c^16)::
on line {185,1986}.
>The orthologic center (N1N2N3, A'B'C') is the NPC center of A'B'C'
X(143).
Best regards,
Peter Moses.
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