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) = (s2 - r2)cos A - (s2 + r2)cos(B - C) - 2rs sin A (Peter J. C. Moses)
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = 1/[a3 - a(b2 - bc + c2) - bc(b + c)] (Paul Yiu)
X(2051) is the external center of similitude of the nine-point and Apollonius circles. Trilinears for the internal center, X(10), result from g(a,b,c) by changing the "-" just after "cos A" to "+". (The two circles are described just before X(1662).)
X(2051) lies on these lines:
2,573 4,386 5,10 6,2050 11,181 12,1682 27,275 43,1699 226,1465 321,908 469,2052 485,1685 486,1686 572,2185 1348,1693 1349,1694 1676,1683 1677,1684 1695,1698 1766,2339 2009,2019 2101,2020 2037,2040