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

X(667)
(CROSSDIFFERENCE OF X(2) AND X(37))


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) = a2(b - c)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(667) = radical center of the circumcircle, Brocard circle, and the circle with (diameter = segment X(1)X(3)) (Wilson Stothers, 3/31/2003)

X(667) lies on these lines:
3,1083    36,238    56,764    100,898    101,813    187,237    213,875    514,659    656,832    668,932    692,1110    788,798

X(667) = midpoint of X(649) and X(663)
X(667) = isogonal conjugate of X(668)
X(667) = inverse-in-circumcircle of X(1083)
X(667) = X(I)-Ceva conjugate of X(J) for these (I,J): (100,6), (101,213)
X(667) = crosspoint of X(I) and X(J) for these (I,J): (6,100), (58,101)
X(667) = crosssum of X(I) and X(J) for these (I,J): (2,513), (10,514), (75,693), (100,1332), (120,918), (523,1211), (850,1234)

X(667) = crossdifference of any two points on line X(2)X(37)

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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