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 bc/(a^{2} - 2b^{2} - 2c^{2}) : ca/(b^{2} - 2c^{2} - 2a^{2}) : ab/(c^{2} - 2a^{2} - 2b^{2})
Barycentrics 1/(a^{2} - 2b^{2} - 2c^{2}) : 1/(b^{2} - 2c^{2} - 2a^{2}) : 1/(c^{2} - 2a^{2} - 2b^{2})The Lemoine ellipse is the ellipse inscribed in triangle ABC having X(2) and X(6) as foci. Let A' be where this ellipse meets sideline BC, and define B' and C' cyclically. Then triangles ABC and A'B'C' are perspective, and their perspector is X(598). (Bernard Gibert, 1/5/01, Hyacinthos #2334)
X(598) lies on these lines: 2,187 4,575 6,671 30,262 76,524 98,381
X(598) = isogonal conjugate of X(574)
X(598) = isotomic conjugate of X(599)