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

X(2361)
(X(2)-ISOCONJUGATE OF X(2006))


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.

The JRE (Java Runtime Environment) is not enabled in your browser!

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            a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b), where f(a,b,c) is as in X(2006)
Trilinears            cos(A/2) cos(3A/2) : cos(B/2) cos(3B/2) : cos(C/2) cos(3C/2)      (M. Iliev, 4/12/07)
Trilinears            cos A + cos 2A : cos B + cos 2B : cos C + cos 2C      (M. Iliev, 4/12/07)

Barycentrics    a2/f(a,b,c) : b2/f(b,c,a): c2/f(c,a,b)

X(2361) lies on these lines:
3,47    6,31    11,238    36,1464    44,2342    46,582    56,255    65,580    109,1155    162,243    228,2148    283,2148    283,960    484,1718    517,1411    518,1331    652,663    920,1062    1040,1707    1110,2149    1397,2352    1724,1837    1754,1836    1780,1858    1859,2299    2150,2193

X(2361) = X(I)-Ceva conjugate of X(J) for these I,J: 80,2174    102,48    2316,41    2342,55
X(2361) = crosspoint of X(I) and X(J) for these I,J: 36,2323    915,1172
X(2361) = crosssum of X(I) and X(J) for these I,J: 36,2003    65,1465    80,2006    912,1214

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



free counter