[Antreas P. Hatzipolakis]:
Let ABC be a triangle and A'B'C' the cevian triangle of H.
Denote:
Bc, Cb = the orthogonal projections of B',C' on CC', BB', resp.
(Nbc), (Ncb) = the NPCs of right angled triangles BcHB', CbHC', resp.
R1 = the radical axis of (Nbc), (Ncb).
Similarly R2, R3
A*B*C* = the triangle bounded by R1, R2, R3
ABC, A*B*C* are parallelogic.
The parallelogic center (ABC, A*B*C*) is the N.
The other one (A*B*C*, ABC) ?
Denote:
Bc, Cb = the orthogonal projections of B',C' on CC', BB', resp.
(Nbc), (Ncb) = the NPCs of right angled triangles BcHB', CbHC', resp.
R1 = the radical axis of (Nbc), (Ncb).
Similarly R2, R3
A*B*C* = the triangle bounded by R1, R2, R3
ABC, A*B*C* are parallelogic.
The parallelogic center (ABC, A*B*C*) is the N.
The other one (A*B*C*, ABC) ?
[Peter Moses]:
Hi Antreas,
a^2 (6 a^6 b^2-18 a^4 b^4+18 a^2 b^6-6 b^8+6 a^6 c^2-34 a^4 b^2 c^2-21 a^2 b^4 c^2+49 b^6 c^2-18 a^4 c^4-21 a^2 b^2 c^4-86 b^4 c^4+18 a^2 c^6+49 b^2 c^6-6 c^8)::
on lines {{140,14845},{3850,5446},{12111,13451}}.
5 X[3850] + 3 X[5446], 11 X[3850] - 3 X[11591], 11 X[5446] + 5 X[11591], 7 X[3850] + X[13421], X[12111] + 15 X[13451].
Best regards,
Peter Moses.
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