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 f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos(A + ω) - sin A
= sin(A + ω) - cos A;Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
X(1689) is the external center of similitude of the Gallatly circle and the circumcircle. (Peter J. C. Moses, 9/03)
X(1689) lies on these lines: 1,2018 2,2009 3,6 4,2010 55,2007 56,2008 165,2017 958,2013 1344,2015 1345,2016 1376,2014
X(1689) = reflection of X(1690) in X(6)
X(1689) = inverse-in-Brocard-circle of X(1687)
X(1689) = X(262)-Ceva conjugate of X(1690)