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

X(1458)
(X(518)-BETH CONJUGATE OF X(518))


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(518)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1458) lies on these lines:
1,7    3,1037    6,41    31,222    36,59    38,1214    42,57    55,1407    64,963    65,1418    108,1430    109,840    185,1208    223,614    238,651    241,518    244,1465    256,1476    354,1427    513,663    672,1362    919,1416    942,1254    976,1038    999,1064    1201,1419    1401,1402    1429,1462

X(1458) = X(I)-Ceva conjugate of X(J) for these (I,J): (241,672), (1477,56)
X(1458) = crosspoint of X(I) and X(J) for these (I,J): (1,103)
X(1458) = crosssum of X(1) and X(516)
X(1458) = crossdifference of any two points on line X(9)X(522)
X(1458) = X(I)-Hirst inverse of X(J) for these (I,J): (6,56), (6,72)

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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