INSTITUTO DE MATEMÁTICA
HJB --- GMA --- UFF

X(1407)
(X(57)-BETH CONJUGATE OF X(57))


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: tc.zip (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) = (1 - cos A)u(a,b,c), where u : v : w = X(57)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1407) lies on these lines:
3,951    6,57    7,940    31,56    34,1413    55,1458    63,220    73,1466    81,279    109,1477    189,1146    278,1086    478,1122    479,1462    534,553    608,1435    614,1456    739,934    942,1448    1104,1394    1119,1396    1333,1412    1357,1397    1398,1408    1401,1460    1464,1470

X(1407) = isogonal conjugate of X(346)
X(1407) = X(I)-Ceva conjugate of X(J) for these (I,J): (269,56), (1119,1398), (1262,1461), (1275,934), (1396,1435)
X(1407) = X(I)-cross conjugate of X(J) for these (I,J): (604,56), (608,1413), (1042,269)
X(1407) = cevapoint of X(604) and X(1106)
X(1407) = crosspoint of X(I) and X(J) for these (I,J): (57,1422), (269,738), (279,1119), (934,1275), (1262,1461), (1396,1412)
X(1407) = crosssum of X(I) and X(J) for these (I,J): (200,728), (220,1260)

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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