HJB --- GMA --- UFF


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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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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) = a -5(b -3 - c -3) + a -4(b -4 - c -4)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

As the isogonal conjugate of a point on the circumcircle, X(768) lies on the line at infinity. The first trilinear coordinate has the form

am-1(bn - cn) + an-1(bm - cm),

corresponding to an odd polynomial center in case m and n are distinct integers. See the note accompanying X(696), where even (m,n) infinity points and even (m,n) circumcircle points are introduced. [For nonzero n, "odd (m,n) circumcircle point" would be a misnomer (as the point is an even polynomial center); consequently, the prefix o- is used to distinguish this point from "even (m,n) circumcircle point" defined at X(696).] Certain points of these classes occur prior to this section. They are as follows:

       X(523) = odd (- 4, - 2) infinity point
       X(688) = odd (- 4, 0) infinity point
       X(689) = o-(- 4, 0) circumcircle point
       X(514) = odd (- 2, - 1) infinity point
       X(101) = o-(- 2, - 1) circumcircle point
       X(512) = odd (- 2, 0) infinity point
       X(99) = o-(- 2, 0) circumcircle point
       X(513) = odd (- 1, 0) infinity point
       X(100) = o-(- 1, 0) circumcircle point
       X(514) = odd (0, 1) infinity point
       X(101) = o-(0, 1) circumcircle point
       X(523) = odd (0, 2) infinity point
       X(110) = o-(0, 2) circumcircle point
       X(513) = odd (1, 2) infinity point
       X(100) = o-(1, 2) circumcircle point
       X(512) = odd (2, 4) infinity point
       X(99) = o-(2, 4) circumcircle point

X(768) lies on this line: 30,511

X(768) = isogonal conjugate of X(769)

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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