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) = 1/[cos A + 2 cos(B - ω) cos(C - ω)]
Barycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)Let P be the point where the line through X(6) parallel to line CA meets line BC, and let Q be the point where the line through X(6) parallel to line AB meets line BC. Let X = X(39), and let A' be the circumcenter of the triangle PQX. Define B' and C' cyclically. The lines AA', BB', CC' concur in X(592). (Floor van Lamoen, 1/4/01)