HYACINTHOS 25287

[Antreas P. Hatzipolakis]:

 

 

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

Denote:

A1, B1, C1 = the reflections of I in BC, CA, AB, resp.

A2, B2, C2 = the reflections of A', B', C' in B'C', C'A', A'B', resp.

The circumcircles of IA1A2, IB1B2, IC1C2 are coaxial.

2nd point of intersection?

[Peter Moses]:

Hi Antreas,

 

3 a^5 b-a^4 b^2-4 a^3 b^3+a b^5+b^6+3 a^5 c+6 a^4 b c-a^3 b^2 c-2 a^2 b^3 c-4 a b^4 c-2 b^5 c-a^4 c^2-a^3 b c^2+4 a^2 b^2 c^2+3 a b^3 c^2-b^4 c^2-4 a^3 c^3-2 a^2 b c^3+3 a b^2 c^3+4 b^3 c^3-4 a b c^4-b^2 c^4+a c^5-2 b c^5+c^6::
on line {1,7},
Search -2. 46101404593507493932252667316.

 

Best regards,

Peter Moses.