HJB --- GMA --- UFF


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: (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           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (cos A)(1 + csc A sin B sin C) + cos B cos C
Trilinears            sin(A + π/4)csc2A : sin(B + π/4)csc2B : sin(C + π/4)csc2C      (M. Iliev, 4/12/07)
Trilinears            (1 + cot A) csc A : (1 + cot B) csc B : (1 + cot C) csc C      (M. Iliev, 4/12/07)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
Barycentrics    b2 + c2 - a2 + 4σ) : c2 + a2 - b2 + 4σ) : a2 + b2 - c2 + 4σ)       (M. Iliev, 5/13/07)

X(492) is a pole associated with squares that circumscribe ABC. For details and reference, see X(488). (Floor van Lamoen, 4/27/98)

X(492) lies on these lines: 2,6    3,489    4,488    5,638    76,486    315,372    371,641    487,631

X(492) = isotomic conjugate of X(485)
X(492) = anticomplement of X(590)
X(492) = X(264)-Ceva conjugate of X(491)
X(492) = cevapoint of X(2) and X(488)

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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