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           bc(v + w) : ca(w + u) : ab(u + v), where
                                    u : v : w = X(284); e.g., u(A,B,C) = (sin A)/(cos B + cos C)
Barycentrics    v + w : w + u : u + v

Let Ia, Ib, Ic be the excenters, let Ab, Ac be the projections of A onto IaIb and IaIc, respectively, and define Bc, Ba and Ca, Cb cyclically. The Euler lines of the four triangles ABC, AAbAc, BBcBa, CCaCb concur in X(442). (Jean-Pierre Ehrmann, 11/24/01)

X(442) lies on these lines: 2,3    8,495    9,46    10,12    11,214    100,943    115,120    119,125    274,325    388,956    392,946

X(442) = midpoint of X(79) and X(191)
X(442) = isogonal conjugate of X(1175)
X(442) = inverse-in-orthocentroidal-circle of X(405)
X(442) = complement of X(21)
X(442) = complementary conjugate of X(960)
X(442) = X(100)-Ceva conjugate of X(523)
X(442) = crosspoint of X(264) and X(321)
X(442) = crosssum of X(184) and X(1333)

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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