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.
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 1703,2017X(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)