## X(2010) (EXSIMILICENTER(GALLATLY 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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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(2010) lies on these lines:
2,1690    4,1689    5,39    10,2019    11,2008    12,2007    83,1687    98,1688    485,1671    486,1670    1346,2015    1347,2016    1348,2011    1349,2012    1698,2017    1699,2018    2026,2039    2027,2040

X(2010) = reflection of X(2009) in X(115)
X(2010) = isogonal conjugate of X(1688)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.