## X(2006) (ORTHOCORRESPONDENT OF X(80))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = yz + (-x cos A + y cos B + z cos C)x, where x : y : z = X(80)
Trilinears           sin(A/2) sec(3A/2) : sin(B/2) sec(3B/2) : sin(C/2) sec(3C/2)      (M. Iliev, 4/12/07)
Trilinears           (tan A/2)/(1 - 2 cos A) : (tan B/2)/(1 - 2 cos B): (tan C/2)/(1 - 2 cos C)      (M. Iliev, 4/12/07)
Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = bc/[(b + c - a)(b2 + c2 - a2 - bc)]      (M. Iliev, 5/13/07)

Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2006) lies on these lines:
1,5    7,89    28,108    57,1020    79,1399    81,226    88,655    274,349    1427,1989    1758,1929

X(2006) = isogonal conjugate of X(2323)
X(2006) = cevapoint of X(1400) and X(1457)
X(2006) = X(2)-beth conjugate of X(651)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.