## X(1670) (INVERSE-IN-BROCARD-CIRCLE OF X(1342))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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 cot(ω/2) : sin B - cos B cot(ω/2) : sin C - cos C cot(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)
= cos(A + ω/2) : cos(B + ω/2) : cos(C + ω/2)

X(1670) is the external center of similitude of the Gallatly circle and the 2nd Lemoine circle. (Peter J. C. Moses, 9/03; cf. X(1342))

X(1670) lies on these lines:
3,6    76,1677    262,1676    485,2009    486,2010    1124,2007    1335,2008    1377,2013    1378,2014    1702,2017    1703,2018

X(1670) = reflection of X(1671) in X(3)
X(1670) = inverse-in-Brocard-circle of X(1342)
X(1670) = X(76)-Ceva conjugate of X(1671)

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