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) = - a2 + b2 + c2 + bc + ca + ab
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a f(a,b,c)This point solves a problem posed by Antreas Hatzipolakis in Hyacinthos #3001, June 11, 2001. For the construction as a Sharygin point, see the description at X(1281).
X(846) lies on these lines: 1,21 2,1054 6,1051 9,43 35,228 37,171 55,984 100,756 333,740 405,986 982,1001
X(846) = X(I)-Ceva conjugate of X(J) for these (I,J): (37,1), (171,43)