## X(108) (Ψ(CIRCUMCENTER, ORTHOCENTER))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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Download all construction files and macros: tc.zip (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           a/(sec B - sec C) : b/(sec C - sec A): c/(sec A - sec B)
= g(a,b,c) : g(b,c,a) : g(c,a,b) where g(a,b,c) = 1/[(b - c)(b + c - a)(b2 + c2 - a2)]

Barycentrics    a2/(sec B - sec C) : b2/(sec C - sec A): c2/(sec A - sec B)

X(108) = Ψ(X(3), X(1))
X(108) = Ψ(X(1), X(4))

X(108) lies on these lines:
1,102    2,123    4,11    7,1013    12,451    24,915    25,105    28,225    33,57    34,106    40,207    55,196    65,74    99,811    100,653    109,1020    110,162    204,223    273,675    318,404    331,767    388,406    429,961    608,739    648,931

X(108) = reflection of X(1295) in X(3)
X(108) = isogonal conjugate of X(521)
X(108) = anticomplement of X(123)
X(108) = X(162)-Ceva conjugate of X(109)
X(108) = cevapoint of X(I) and X(J) for these (I,J): (56,513), (429,523)
X(108) = X(513)-cross conjugate of X(4)
X(108) = crosspoint of X(107) and X(162)
X(108) = crosssum of X(520) and X(656)
X(108) = X(I)-beth conjugate of X(J) for these (I,J): (21,102), (162,108)

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

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense