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

X(2489)
(RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE})


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) = a(b2 - c2)/(b2 + c2 - a2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2489) lies on these lines:
6,924    19,876    112,250    230,231    393,2395    512,1692    520,2451    882,1843    1974,2422    2507,2524

X(2489) = reflection of X(I) in X(J) for these I,J: 647,2485    2485,2492    2524,2507
X(2489) = X(112)-Ceva conjugate of X(25)
X(2489) = cevapoint of X(647) and X(2519)
X(2489) = X(I)-cross conjugate of X(J) for these I,J: 669,512    1084,1974
X(2489) = crosspoint of X(25) and X(112)

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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