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

X(1724)
(MIMOSA TRANSFORM OF X(58))


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(58)
Trilinears           a2(a + b + c) - bc(b + c) : b2(a + b + c) - ca(c + a) : c2(a + b + c) - ab(a + b)       (M. Iliev, 5/13/07)

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

X(1724) lies on these lines:
1,6    2,58    4,580    8,595    10,31    21,286    28,579    30,582    32,1009    34,1708    35,43    36,978    46,1707    47,1737    83,1008    90,1039    109,1788    171,1698    191,986    212,950    226,1451    255,1210    270,469    387,452    515,602    581,1006    748,1125    920,1735    985,1224    993,1193    1020,1398    1445,1448    1726,1829    1738,1770

X(1724) = X(I)-Ceva conjugate of X(J) for these (I,J): (28,1), (579,1754), (1778,1707)
X(1724) = crosspoint of X(162) and X(765)
X(1724) = crosssum of X(244) and X(656)
X(1724) = X(I)-aleph conjugate of X(J) for these (I,J): (4,1710), (27,1730), (28,1724), (266,1047)

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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