## X(672) (CROSSDIFFERENCE OF X(1) AND X(514))

 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 - a(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(672) lies on these lines:
1,1002    2,7    3,41    6,31    36,101    37,38    39,213    43,165    44,513    46,169    56,220    72,1009    103,919    105,238    190,350    219,604    519,1018

X(672) = isogonal conjugate of X(673) X(672) = X(I)-Ceva conjugate of X(J) for these (I,J): (103,55), (291,42)
X(672) = crosspoint of X(I) and X(J) for these (I,J): (6,292), (241,518)
X(672) = crosssum of X(I) and X(J) for these (I,J): (1,672), (2,239), (105,294)
X(672) = crossdifference of any two points on line X(1)X(514)
X(672) = X(I)-Hirst inverse of X(J) for these (I,J): (6,55), (1362,1458)

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