HYACINTHOS 25212

[Antreas P. Hatzipolakis]:

Let ABC be a triangle.

Denote:

Na, Nb, Nc = the NPC centers of IBC, ICA, IAB, resp.

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

The circumcircles of IA'Na, IB'Nb, IC'Nc are coaxial.

Second point of intersection?

[Peter Moses]:

Hi Antreas,

 

4 a^10-15 a^9 b+5 a^8 b^2+38 a^7 b^3-38 a^6 b^4-24 a^5 b^5+44 a^4 b^6-6 a^3 b^7-14 a^2 b^8+7 a b^9-b^10-15 a^9 c+62 a^8 b c-64 a^7 b^2 c-58 a^6 b^3 c+154 a^5 b^4 c-68 a^4 b^5 c-56 a^3 b^6 c+62 a^2 b^7 c-19 a b^8 c+2 b^9 c+5 a^8 c^2-64 a^7 b c^2+180 a^6 b^2 c^2-121 a^5 b^3 c^2-119 a^4 b^4 c^2+187 a^3 b^5 c^2-69 a^2 b^6 c^2-2 a b^7 c^2+3 b^8 c^2+38 a^7 c^3-58 a^6 b c^3-121 a^5 b^2 c^3+286 a^4 b^3 c^3-125 a^3 b^4 c^3-62 a^2 b^5 c^3+50 a b^6 c^3-8 b^7 c^3-38 a^6 c^4+154 a^5 b c^4-119 a^4 b^2 c^4-125 a^3 b^3 c^4+166 a^2 b^4 c^4-36 a b^5 c^4-2 b^6 c^4-24 a^5 c^5-68 a^4 b c^5+187 a^3 b^2 c^5-62 a^2 b^3 c^5-36 a b^4 c^5+12 b^5 c^5+44 a^4 c^6-56 a^3 b c^6-69 a^2 b^2 c^6+50 a b^3 c^6-2 b^4 c^6-6 a^3 c^7+62 a^2 b c^7-2 a b^2 c^7-8 b^3 c^7-14 a^2 c^8-19 a b c^8+3 b^2 c^8+7 a c^9+2 b c^9-c^10:: on line {1,6952}.

Search -0. 293090788033271397785460216612

 

Best regards,

Peter Moses.