HYACINTHOS 23831

[Tran Quang Hung]:

Let ABC be a triangle and its excenters Ia,Ib,Ic


Denote:


A', B', C' = the reflections of Ia,Ib,Ic in BC, CA, AB, resp.


A", B", C" = the reflections of Ia,Ib,Ic in A', B', C', resp.


The Euler lines of A"BC, B"CA, C"AB are concurrent.

 

[Angel Montesdeoca]:

*** They intersect at W=(7a^3-a^2(b+c)-a(4b^2+b c+4c^2)-2(b-c)^2(b+c) : ... : ...)

On lines {8, 30}, {21, 551}, {79, 3634}, {191, 6175}, {527, 2346}, {553, 5284}, {1281, 6054}, {2796, 4921}, {2975, 3656}, {3624, 3647}


Search numbers (7.24647969768325, 4.60988537952130, -2.89532371823033)

Angel M.