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) = (sin A/4)/sin(3A/4)
Trilinears gA,B,C) : g(B,C,A) : g(C,A,B),
where g(A,B,C) = [1 - 2 cos(A/2)]/(1 + 2 cos A) (M. Iliev, 5/13/07)
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
Let A', B', C' be the incenters of triangles XBC, XCA, XAB, respectively, where X is the incenter, X(1). The triangle A'B'C' is perspective to ABC, and the perspector is X(1127). Coordinates found by Darij Grinberg, 8/22/02.
Michael de Villiers, A dual to Kosnita's theorem, reprinted from Mathematics & Informatics Quarterly 6 (1996) 1996.
X(1127) lies on this line: 174,481
X(1127) = isogonal conjugate of X(1129)