## X(1671) (INVERSE-IN-BROCARD-CIRCLE OF X(1343))

 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           sin A + cos A tan(ω/2) : sin B + cos B tan(ω/2) : sin C + cos C tan(ω/2)
= sin A + sin(A + ω) : sin B + sin(B + ω) : sin C + sin(C + ω)
= cos A - cos(A + ω) : cos B - cos(B + ω) : cos C - cos(C + ω)
= sin(A + ω/2) : sin(B + ω/2) : sin(C + ω/2)

X(1671) is the internal center of similitude of the Gallatly circle and the 2nd Lemoine circle. (Peter J. C. Moses, 9/03)

X(1671) lies on these lines:
3,6    76,1676    262,1677    485,2010    486,2009    1124,2008    1335,2007    1377,2014    1378,2013    1702,2018    1703,2017

X(1671) = reflection of X(1670) in X(3)
X(1671) = inverse-in-Brocard-circle of X(1343)
X(1671) = X(76)-Ceva conjugate of X(1670)

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