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) = yz + (-x cos A + y cos B + z cos C)x, where x : y : z = X(80)
Trilinears sin(A/2) sec(3A/2) : sin(B/2) sec(3B/2) : sin(C/2) sec(3C/2) (M. Iliev, 4/12/07)
Trilinears (tan A/2)/(1 - 2 cos A) : (tan B/2)/(1 - 2 cos B): (tan C/2)/(1 - 2 cos C) (M. Iliev, 4/12/07)
Trilinears g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = bc/[(b + c - a)(b2 + c2 - a2 - bc)] (M. Iliev, 5/13/07)Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
X(2006) lies on these lines:
1,5 7,89 28,108 57,1020 79,1399 81,226 88,655 274,349 1427,1989 1758,1929X(2006) = isogonal conjugate of X(2323)
X(2006) = cevapoint of X(1400) and X(1457)
X(2006) = X(2)-beth conjugate of X(651)