HYACINTHOS 23949

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Antreas P. Hatzipolakis

 

 

[APH]:

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

Denote:

Ab = the orthogonal projection of A' on BB"
Abc = the orthogonal projection of Ab on CC'

Ac = the orthogonal projection of A' on CC'
Acb = the orthogonal projection of Ac on BB'

L1 = the Euler line of IAbcAcb

Similarly L2 = the Euler line of IBcaBac, L3 = the Euler line of ICabCba

The L1, L2, L3 are concurrent ??

 

[Angel Montesdeoca]:

 

**** The L1, L2, L3 are concurrent in
W=(a (a^4 (b-c)^2-a^2 (b^4+7 b^3 c+16 b^2 c^2+7 b c^3+c^4)-a (b^5+b^4 c+8 b^3 c^2+8 b^2 c^3+b c^4+c^5)+b c (b^2-c^2)^2+a^3 (b^3-7 b^2 c-7 b c^2+c^3)):...:....)

with (6-9-13)-search number (1. 8214877770399515195893339456
On lines:  {500,1066}, {511,5045}, {524,5044}, {3945,5752}

Angel Montesdeoca