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 (tan A/2 sec A/2)^{2} : (tan B/2 sec B/2)^{2} : (tan C/2 sec C/2)^{2}
Barycentrics tan^{3}(A/2) : tan^{3}(B/2) : tan^{3}(C/2)
= 1/(b + c - a)^{3} : 1/(c + a - b)^{3} : 1/(a + b - c)^{3}Let A' be the point in which the incircle is tangent to a circle that passes through vertices B and C, and define B' and C' cyclically. The lines AA', BB', CC' concur in X(479)
Clark Kimberling and Peter Yff, Problem 10678, American Mathematical Monthly 105 (1998) 666.
X(479) lies on these lines: 7,354 57,279 269,614
X(479) = isogonal conjugate of X(480)
X(479) = X(269)-cross conjugate of X(279)