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) = 1/[a(b2 - c2)(b2 + c2 - a2)]
                                    = u(A,B,C) : u(B,C,A) : u(C,A,B), where u(A,B,C) = csc 2A csc(B - C)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(648) is constructed as the pole of the Euler line L as follows: let A", B", C" be the points where L meets the sidelines BC, CA, AB of the reference triangle ABC. Let A', B', C' be the harmonic conjugates of A", B", C" with respect to {B,C}, {C,A}, {A,B}, respectively, The lines AA', BB', CC' concur in X(648).

X(648) lies on these lines:
4,452    6,264    27,903    94,275    95,216    99,112    107,110    108,931    132,147    155,1093    162,190    185,1105    193,317    232,385    249,687    250,523    297,340    447,519    645,668    651,823    653,662    925,933    1020,1021    1075,1092

X(648) = reflection of X(I) in X(J) for these (I,J): (287,6), (340,297), (1494,2)
X(648) = isogonal conjugate of X(647)
X(648) = isotomic conjugate of X(525)
X(648) = cevapoint of X(110) and X(112)
X(648) = X(I)-cross conjugate of X(J) for these (I,J): (6,250), (110,99), (112,107), (520,95), (523,264)

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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