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           a3/(b2 - c2) : b3/(c2 - a2) : c3/(a2 - b2)
Barycentrics    a4/(b2 - c2) : b4/(c2 - a2) : c4/(a2 - b2)

X(1576) is the perspector of the excentral triangle and the apices of equilateral triangles constructed outward from the sides, as in the construction of X(13). (Paul Yiu, 2/27/04).

X(1576) lies on these lines:
3,1177    6,157    32,1084    50,237    99,827    107,933    110,351    160,206    163,692    250,523    338,1316    662,1492

X(1576) = midpoint of X(648) and X(1632)
X(1576) = isogonal conjugate of X(850)
X(1576) = X(I)-Ceva conjugate of X(J) for these (I,J): (249,1501), (250,6), (827,110), (933,112)
X(1576) = cevapoint of X(I) and X(J) for these (I,J): (32,669), (39,647), (51,512)
X(1576) = X(I)-cross conjugate of X(J) for these (I,J): (669,32), (1501,249)
X(1576) = crosspoint of X(110) and X(112)
X(1576) = crosssum of X(523) and X(525)
X(1576) = crossdifference of any two points on line X(115)X(127)

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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