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 1/(1 + 2 cos A) : 1/(1 + 2 cos B) : 1/(1 + 2 cos C)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/(b2 + c2 - a2 + bc)
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A/2)(sin 3B/2)(sin 3C/2)
Barycentrics h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = 1/(b2 + c2 - a2 + bc)
Let A' be the reflection of X(1) in sideline BC, and define B' and C' cyclically. Then the lines AA', BB', CC' concur in X(79). (Eric Danneels, Hyacinthos 7892, 9/13/03)
X(79) lies on these lines:
1,30 8,758 9,46 12,484 21,36 33,1063 34,1061 35,226 57,90 65,80 104,946 314,320 388,1000
X(79) = reflection of X(191) in X(442)
X(79) = isogonal conjugate of X(35)
X(79) = isotomic conjugate of X(319)
X(79) = cevapoint of X(481) and X(482)
X(79) = crosssum of X(55) and X(1030)