HYACINTHOS 22710

 

 

 

Antigonal Conjugate of I wrt cevian triangle of I (incentral triangle).

Barycentrics: (a^2 (a^5 + a^4(b+c) - 2a^3(b^2+c^2) -  a^2(2b^3-b*c(b+c)+2c^3)+ a(b^4+b^2c^2+c^4) + (b-c)^2(b^3+c^3))

 
3R X(1) + 2r X(399)
search number 0.812149174855219822306671631

(Angel Montesdeoca, Hyacinthos #22708)

X(1)-Ceva conjugate of X(36)
QA-P41 ('Involutary Conjugate of QA-P4') of quadrangle ABCX(1)
The point P for which P of the 'orthocentroidal triangle' = X(1).
It lies on lines {1,399} {6,1718} {35,73} {36,1464} (at least).

(Randy Hutson, Hyacinthos #21651, 22709)

It lies on the O'I line, where O' is the circumcenter of the incentral triangle
(Shapi Topor, In "Short Math. Idea", Hyacinthos #22707)

 

APH