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) = bc(-a^{2} + b^{2} + c^{2} + bc + ca + ab)
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = -a^{2} + b^{2} + c^{2} + bc + ca + abLet P be a point in the plane of, but not on a sideline of, triangle ABC. Let B_{a} be the point where the line through P parallel to line BC meets line BA, and let C_{a} be the point where the line through P parallel to line BC meets line CA. Define C_{b}, A_{b}, A_{c}, and B_{c} cyclically. If P = X(1654), then
|AB_{a}| + |AC_{a}| = |BC_{b}| + |BA_{b}| = |CA_{c}| + |CB_{c}| (Antreas Hatzipolakis, Anopolis #20, 1/20/02)
X(1654) lies on these lines: 2,6 8,192 10,894 37,319 71,1762 190,594
X(1654) = reflection of X(86) in X(1213)
X(1654) = anticomplement of X(86)
X(1654) = X(I)-Ceva conjugate of X(J) for these (I,J): (10,2), (894,192)