HYACINTHOS 25373

[Antreas P. Hatzipolakis]:

 

Let ABC be a triangle.

Denote:

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

Ma, Mb, Mc = the midpoints of AA', BB', CC', resp.

M1, M2, M3 = the reflections of Ma, Mb, Mc in BC, CA, AB, resp.

The circumcircles of AIM1, BIM2, CIM3 are coaxial.

2nd point of intersection ?

[Peter Moses]:

Hi Antreas,

 

a (a^3+3 a^2 b+3 a b^2+b^3+a^2 c+a b c+b^2 c-a c^2-b c^2-c^3) (a^3+a^2 b-a b^2-b^3+3 a^2 c+a b c-b^2 c+3 a c^2+b c^2+c^3) (2 a^5+a^4 b-4 a^3 b^2-2 a^2 b^3+2 a b^4+b^5+a^4 c-4 a^3 b c-a^2 b^2 c+3 a b^3 c+b^4 c-4 a^3 c^2-a^2 b c^2+4 a b^2 c^2-2 b^3 c^2-2 a^2 c^3+3 a b c^3-2 b^2 c^3+2 a c^4+b c^4+c^5)::
on line {{1,1030}} and K040,
searches {-2. 58128936239293970224767649241, -2. 11953479944549353241229097517, 6. 29939904878184679582579262027}

 

Best regards,

Peter Moses.