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

X(2009)
(INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT 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) = cos(B - C) + sin(A + ω)
Trilinears           h(A,B,C) : h(B,C,A): h(C,A,B), where h(A,B,C) = csc(A - ω/2 + π/4)       (M. Iliev, 5/13/07)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(2009) lies on these lines:
2,1689    4,1690    5,39    10,2020    11,2007    12,2008    83,1688    98,1687    485,1670    486,1671    1346,2016    1347,2015    1348,2012    1349,2011    1698,2018    1699,2017    2026,2040    2027,2039

X(2009) = reflection of X(2010) in X(115)
X(2009) = isogonal conjugate of X(1687)

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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