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            2 - cos A : 2 - cos B : 2 - cos C (Joe Goggins, 2002)
                                    = f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a(a2 + 4bc - b2 - c2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(999) lies on these lines: 1,3    2,495    4,496    5,388    6,101    7,104    8,474    11,381    12,499    20,1058    30,497    63,392    77,1057    78,1059    81,859    145,404    329,405    376,390    518,997    527,551    601,1106    938,944    954,1006

X(999) is the {X(1),X(56)}-harmonic conjugate of X(3).

X(999) = midpoint of X(1) and X(57)
X(999) = isogonal conjugate of X(1000)
X(999) = X(89)-Ceva conjugate of X(6)
X(999) = crossdifference of any two points on line X(650)X(900)

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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