INSTITUTO DE MATEMÁTICA
HJB --- GMA --- UFF

X(108)
(Ψ(CIRCUMCENTER, ORTHOCENTER))


Click here to access the list of all triangle centers.

Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon Run Macro Tool, select the center name from the list and, then, click on the vertices A, B and C successively.

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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



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