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           ab + ac - bc : bc + ba - ca : ca + cb - ab
                                    = csc B + csc C - csc A : csc C + csc A - csc B : csc A + csc B - csc C

Barycentrics    a(ab + ac - bc) : b(bc + ba - ca) : c(ca + cb - ab)

X(43) lies on these lines:
1,2    6,87    9,256    31,100    35,1011    40,970    46,851    55,238    57,181    58,979    72,986    75,872    81,750    165,573    170,218    210,984    312,740    518,982

X(43) is the {X(2),X(42)}-harmonic conjugate of X(1).

X(43) = reflection of X(1) in X(995)
X(43) = isogonal conjugate of X(87)
X(43) = X(6)-Ceva conjugate of X(1)
X(43) = X(192)-cross conjugate of X(1)
X(43) = crosssum of X(2) and X(330)
X(43) = X(55)-Hirst inverse of X(238)

X(43) = X(I)-aleph conjugate of X(J) for these (I,J):
(1,9), (6,43), (55,170), (100,1018), (174,169), (259,165), (365,1), (366,63), (507,362), (509,57)

X(43) = X(660)-beth conjugate of X(43)

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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