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 sin^{2}A csc 3A : sin^{2}B csc 3B : sin^{2}C csc 3C
Barycentrics sin^{3}A csc 3A : sin^{3}B csc 3B : sin^{3}C csc 3CX(1989) plays a major role in the theory of special isocubics, as presented in Chapter 6 of
Jean-Pierre Ehrmann and Bernard Gibert,, "Special Isocubics in the Triangle Plane," downloadable from
Bernard Gibert, Cubics in the Triangle Plane.
X(1989) is the barycentric product X(13)*X(14) of the Fermat points. The line through X(50) parallel to
the line X(13)X(14) passes through X(1989).
X(1989) lies on these lines:
2,94 6,13 30,50 53,112 67,868 111,230 403,1990 1427,2006X(1989) = isogonal conjugate of X(323)
X(1989) = complement of X(1272)
X(1989) = X(94)-Ceva conjugate of X(265)
X(1989) = cevapoint of X(I) and X(J) for these (I,J): (53,1990), (115,1637), (395,396)
X(1989) = crosspoint of X(2) and X(1138)
X(1989) = crosssum of X(6) and X(399)
X(1989) = barycentric product of X(13) and X(14)