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 - 2 cos B cos C)2
Barycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A) f(A,B,C)Evans conjectured that X(1), X(484), X(1276), X(1277) are concyclic, and reported that Paul Yiu confirmed this conjecture and noted that the center of this circle is X(1019). (Lawrence Evans, 2/24/2003)
X(1099) lies on these lines: 1,564 75,811 162,255