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

X(1707)
(MIMOSA TRANSFORM OF X(6))


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) = - (cos A)/x + (cos B)/y + (cos C)/z,    x : y : z = X(6)
Trilinears           3a2 - b2 - c2 : 3b2 - c2 - a2 : 3c2 - a2 - b2       (M. Iliev, 5/13/07)

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

X(1707) lies on these lines:
1,21    9,171    19,1719    33,1776    36,1473    43,165    44,1376    46,1722    57,238    92,1733    109,1395    162,1096    200,1757    204,240    223,1758    326,560    380,1045    484,1774    579,1716    580,1158    610,1740    978,1044    986,1453    1038,1399    1633,1732    1709,1711    1714,1770    1728,1771    1788,1877

X(1707) = X(I)-Ceva conjugate of X(J) for these (I,J): (19,1), (1778,1724)
X(1707) = X(I)-aleph conjugate of X(J) for these (I,J): (1,610), (4,19), (19,1707), (108,1783), (162,163), (365,1745), (366,1763), (509,223), (1778,1724), (1783,1633)

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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