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 a/(b + c)^{2} : b/(c + a)^{2} : c/(a + b)^{2}
Barycentrics [a/(b + c)]^{2} : [b/(c + a)]^{2} : [c/(a + b)]^{2}Let O(A) be the circle tangent to line BC and to the circumcircle of triangle ABC at vertex A. Let A_{B} and A_{C} be where O(A) meets lines AB and AC, respectively. Let L(A) be the line joining A_{B} and A_{C}, and define L(B) and L(C) cyclically. Let A' be where L(B) and L(C) meet, and define B' and C' cyclically. Then triangle A'B'C' is homothetic to triangle ABC, and the center of homothety is X(593).
X(593) lies on these lines: 2,261 31,110 36,58 81,757 115,1029 229,1104
X(593) = isogonal conjugate of X(594)
(Antreas Hatzipolakis, Paul Yiu, Hyacinthos #2070)