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) = sqrt(3/4) + sin(A - π/3) - sin(B - π/3) - sin(C - π/3)
= - sqrt(3/4) + cos(A + π/6) - cos(B + π/6) - cos(C + π/6)
Trilinears sqrt(3) tan(A/2) - tan(B/2) tan(C/2) : sqrt(3) tan(B/2) - tan(C/2) tan(A/2) : sqrt(3) tan(C/2) - tan(A/2) tan(B/2) = sqrt(3) tan(A/2) - (b + c - a)/(a + b + c) : sqrt(3) tan(B/2) - (c + a - b)/(a + b + c) : sqrt(3) tan(C/2) - (a + b - c)/(a + b + c) (M. Iliev, 5/13/07)
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
X(1653) is the perspector of the inner Napoleon triangle and the excentral triangle.
X(1653) lies on these lines: 1,16 2,7 46,1276 395,1081 1082,1100
X(1653) = X(I)-Ceva conjugate of X(J) for these (I,J): (1081,1), (2160,1652)
X(1653) = X(1081)-aleph conjugate of X(1653)