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/(2 cos A - τ^{2}sin A), where τ = (1 + sqrt(5))/2 = golden ratio
Trilinears g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sec[A + arccot(3 - 5^{1/2})] (M. Iliev, 5/13/07)Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
In the construction of X(2671), if A' is the center of the s-Archimedean circle of the inward arbelos on segment BC, and B' and C' are defined cyclically, then A'A, B'B, C'C concur in X(2672).
X(2672) lies on the Kiepert hyperbola and these lines: 2,2673 6,2671