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           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 2 cos B cos C - sin(A + ω) csc ω
                                    = g(a,b,c) : g(b,c,a): g(c,a,b), where g(a,b,c) = bc(a4 - b4 - c4 - 2a2b2 - 2a2c2 + 2b2c2)    (Eric Danneels, Nov. 11, 2004)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

The circle (X(4),2R) is identified at X(2474).

X(2549) lies on these lines:
2,99    3,230    4,39    6,30    10,1571    20,32    53,1597    69,538    147,1569    184,1562    187,376    193,754    194,315    388,1500    497,1515    516,1572    625,1007    1194,1370    1478,2276    1479,2275    1504,1587    1505,1588    1573,2550    1574,2551    1885,2207    2033,2542    2034,2543    2035,2546    2036,2547

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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