HYACINTHOS 25214

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle and IaIbIc the antipedal triangle of I.

Denote:

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

The circumcircles of IIaNa, IIbNb, IIcNc are coaxial.

Second point of intersection?

[Peter Moses]:

Hi Antreas,

 

a (2 a^9+3 a^8 b-10 a^7 b^2-10 a^6 b^3+18 a^5 b^4+12 a^4 b^5-14 a^3 b^6-6 a^2 b^7+4 a b^8+b^9+3 a^8 c-2 a^7 b c-20 a^6 b^2 c+16 a^5 b^3 c+32 a^4 b^4 c-26 a^3 b^5 c-16 a^2 b^6 c+12 a b^7 c+b^8 c-10 a^7 c^2-20 a^6 b c^2-6 a^5 b^2 c^2+7 a^4 b^3 c^2-4 a^3 b^4 c^2+17 a^2 b^5 c^2+20 a b^6 c^2-4 b^7 c^2-10 a^6 c^3+16 a^5 b c^3+7 a^4 b^2 c^3-2 a^3 b^3 c^3+5 a^2 b^4 c^3-12 a b^5 c^3-4 b^6 c^3+18 a^5 c^4+32 a^4 b c^4-4 a^3 b^2 c^4+5 a^2 b^3 c^4-48 a b^4 c^4+6 b^5 c^4+12 a^4 c^5-26 a^3 b c^5+17 a^2 b^2 c^5-12 a b^3 c^5+6 b^4 c^5-14 a^3 c^6-16 a^2 b c^6+20 a b^2 c^6-4 b^3 c^6-6 a^2 c^7+12 a b c^7-4 b^2 c^7+4 a c^8+b c^8+c^9)::
on lines {{1,7997},{3579,8701}}.

Search -6.178903573613347826308028238 04.

Reflection of X(i) in X(j) for these {i,j}: {{3579, 8701}}.

 

Best regards,

Peter Moses.