HYACINTHOS 26537

[Tran Quang Hung]:

 

 

Let ABC be a triangle with orthocenter H.

 

Brocard axis of triangle HBC is da.

 

da meets line HA at A'. Similarly, we have B',C'.

 

da meets line B'C' at A''. Similarly, we have B'',C''.

 

Then triangle ABC and A''B''C'' are perspective. Which is the perspector ?

 

 

[Angel Montesdeoca]:

 The perspector of  triangles ABC and A''B''C'' is

W = ((-a^2+b^2-c^2) (a^2+b^2-c^2) (a^4-2 a^2 b^2+b^4-2 a^2 c^2+c^4) (-a^2 b^2+b^4-a^2 c^2-2 b^2 c^2+c^4) (-a^6 b^2+3 a^4 b^4-3 a^2 b^6+b^8-2 a^6 c^2+a^4 b^2 c^2+4 a^2 b^4 c^2-3 b^6 c^2+4 a^4 c^4+a^2 b^2 c^4+3 b^4 c^4-2 a^2 c^6-b^2 c^6) (2 a^6 b^2-4 a^4 b^4+2 a^2 b^6+a^6 c^2-a^4 b^2 c^2-a^2 b^4 c^2+b^6 c^2-3 a^4 c^4-4 a^2 b^2 c^4-3 b^4 c^4+3 a^2 c^6+3 b^2 c^6-c^8) : ... : ....).

W lies on lines X(i)X(j) for these {i, j}: {4,216},  {52,11547},   {324,6750}.
 (6 - 9 - 13) - search numbers  of W: (-0.580799992444424, 0.237807788430956, 3.74408985566037).


Angel Montedeoca