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) = (sec A)[cos(2C - 2A) + cos(2A - 2B)]Trilinears g(A,B,C) : g(B,C,A) : g(C,A,B), where
g(A,B,C) = [1 - 2 cos(2A)]cos(B - C)]Trilinears h(A,B,C) : h(B,C,A) : h(C,A,B), where
h(A,B,C) = sec A cos(3A) cos(B - C) (Manol Iliev, 4/01/07)Barycentrics k(A,B,C) : k(B,C,A) : k(C,A,B), where k(A,B,C) = (tan A)[cos(2C - 2A) + cos(2A - 2B)]
X(143) = X(5)-of-orthic triangle
X(143) lies on these lines: 4,94 5,51 6,26 25,156 30,389 110,195 140,511 324,565
X(143) is the {X(51),X(52)}-harmonic conjugate of X(5).
X(143) = midpoint of X(5) and X(52)
X(143) = isogonal conjugate of X(252)
X(143) = X(137)-cross conjugate of X(1510)