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

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


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           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.

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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