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) = a(b2 + c2 + bc + ca + ab)
Trilinears h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = r cos A + s sin A, s = semiperimeter, r = inradius
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a2(b2 + c2 + bc + ca + ab)
X(386) is the external center of similitude of the circumcircle and Apollonius circle. The internal center is X(573). (Peter J. C. Moses, 8/22/03)
X(386) lies on these lines:
1,2 3,6 31,35 40,1064 55,595 56,181 57,73 65,994 81,404 474,940 758,986 872,984X(386) is the {X(3),X(6)}-harmonic conjugate of X(58).
X(386) = inverse of X(58) in the Brocard circle
X(386) = crosssum of X(6) in X(1011)
X(386) = crossdifference of any two points on line X(523)X(649)