## X(2485) (RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE})

 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 , 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)(b4 + c4 - a4)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2485) lies on these lines:
6,520    230,231    512,1691    525,2507    669,2514    2165,2395

X(2485) = midpoint of X(I) and X(J) for these I,J: 647,2489    669,2514
X(2485) = reflection of X(I) in X(J) for these I,J: 2489,2492    2506,647
X(2485) = X(2)-Ceva conjugate of X(127)
X(2485) = crosspoint of X(I) and X(J) for these I,J: 2,112    83,107
X(2485) = crosssum of X(I) and X(J) for these I,J: 6,525    39,520

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