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[a/(b + c)]^{2} : b[b/(c + a)]^{2} : c[c/(a + b)]^{2}Let D denote the circumcircle of triangle ABC. Let D_{A} be the circle tangent to sideline BC and tangent to D at A. Let B_{a} = AC∩D_{A} and C_{a} = AB∩D_{A}, and define C_{b}, C_{a} and A_{c}, A_{b} cyclically. Define A' = C_{b}A_{b}∩A_{c}B_{c}, and define B' and C' cyclically. Then triangle A'B'C' is homothetic to ABC, and X(849) is the center of homothety. See A. Hatzipolakis and P. Yiu, Hyacinthos #2056-2070, December, 2000.
X(849) lies on these lines: 32,163 36,58 110,595 249,1110 741,827 757,763
X(849) = isogonal conjugate of X(1089)
X(849) = X(249)-Ceva conjugate of X(163)
X(849) = crosspoint of X(58) and X(501)
X(849) = crosssum of X(10) and X(502)