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           csc2A cos(A + ω) : csc2B cos(B + ω) : csc2C cos(C + ω)
                                    = f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc(b4 + c4 - a2b2 - a2c2)

Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = b4 + c4 - a2b2 - a2c2

X(325) lies on these lines:
2,6    3,315    5,76    11,350    22,160    25,317    30,99    39,626    114,511    115,538    187,620    232,297    250,340    264,305    274,442    383,622    523,684    621,1080

X(325) = midpoint of X(I) and X(J) for these (I,J): (99,316), (298,299)
X(325) = reflection of X(I) in X(J) for these (I,J): (115,625), (187,620), (385,230), (1513,114)
X(325) = isogonal conjugate of X(1976)
X(325) = complement of X(385)
X(325) = anticomplement of X(230)
X(325) = cevapoint of X(2) and X(147)
X(325) = X(I)-cross conjugate of X(J) for these (I,J): (114,2), (511,297)
X(325) = crossdifference of any two points on line X(32)X(512)
X(325) = X(2)-Hirst inverse of X(69)

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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