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(1652) is the perspector of the outer Napoleon triangle and the excentral triangle. (See also X(1276) and X(1277).)
X(1652) lies on these lines: 1,15 2,7 46,1277 396,554 559,1100
X(1652) = X(I)-Ceva conjugate of X(J) for these (I,J): (554,1), (2160,1653)
X(1652) = X(554)-aleph conjugate of X(1652)