HYACINTHOS 25749

[Antreas P. Hatzipolakis]:

Let ABC be a triangle.

Denote:

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

Na, Nb, Nc = the NPC centers of NB'C', NC'A', NA'B', resp.

N1, N2, N3 = the orthogonal projections of Na, Nb, Nc on NA', NB', NC', resp.

The NPC center of N1N2N3 lies on the Euler line.

[Peter Moses]:

Hi Antreas,

 

 

2 a^10-3 a^8 b^2-2 a^6 b^4+4 a^4 b^6-b^10-3 a^8 c^2+2 a^6 b^2 c^2-9 a^4 b^4 c^2+7 a^2 b^6 c^2+3 b^8 c^2-2 a^6 c^4-9 a^4 b^2 c^4-14 a^2 b^4 c^4-2 b^6 c^4+4 a^4 c^6+7 a^2 b^2 c^6-2 b^4 c^6+3 b^2 c^8-c^10::
on lines {{2,3},{143,6153},{3574,10272} ,{7693,12254}}.

Midpoint of X(3628) and X(6756).

3 X[428] + X[548], 5 X[546] - X[1885], X[3575] + 3 X[5066], 7 X[3857] + X[6240], 5 X[632] + 3 X[7540], 3 X[140] + X[7553], 5 X[5] + 3 X[7576], 7 X[140] - 3 X[7667], 7 X[7553] + 9 X[7667], X[3530] - 3 X[10127], 3 X[547] + X[11819], 9 X[5] - X[12225], 3 X[10109] - X[12362].

{X(5),X(2070)}-harmonic conjugate of X(140).

 

Not one of the first 13006 ETC points.

 

Best regards,

Peter Moses.