HYACINTHOS 24670

[Antreas P. Hatzipolakis]:

 

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

Denote:

Oa, Ob, Oc = the circumcenters of NB'C', NC'A', NA'B', resp.

Ooa, Oob, Ooc = the circumcenters of NObOc,NOcOa,NOaOb, resp.

The NPC center of OoaOobOoc lies on the Euler line of ABC.

[Peter Moses]:

Hi Antreas,

 

> The NPC center of OoaOobOoc lies on the Euler line of ABC.

2 a^16-13 a^14 b^2+43 a^12 b^4-89 a^10 b^6+115 a^8 b^8-87 a^6 b^10+33 a^4 b^12-3 a^2 b^14-b^16-13 a^14 c^2+62 a^12 b^2 c^2-113 a^10 b^4 c^2+64 a^8 b^6 c^2+61 a^6 b^8 c^2-94 a^4 b^10 c^2+33 a^2 b^12 c^2+43 a^12 c^4-113 a^10 b^2 c^4+68 a^8 b^4 c^4+17 a^6 b^6 c^4+46 a^4 b^8 c^4-81 a^2 b^10 c^4+20 b^12 c^4-89 a^10 c^6+64 a^8 b^2 c^6+17 a^6 b^4 c^6+30 a^4 b^6 c^6+51 a^2 b^8 c^6-64 b^10 c^6+115 a^8 c^8+61 a^6 b^2 c^8+46 a^4 b^4 c^8+51 a^2 b^6 c^8+90 b^8 c^8-87 a^6 c^10-94 a^4 b^2 c^10-81 a^2 b^4 c^10-64 b^6 c^10+33 a^4 c^12+33 a^2 b^2 c^12+20 b^4 c^12-3 a^2 c^14-c^16::

on line {2,3}.

 

Best regards,

PeterMoses.