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) = a[x_{1} - 2Dx_{2}/sqrt(3)], where
D = area(ABC), x_{1}, x_{2} are as at X(1337).Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = a^{2}(2DU + 3^{1/2}VW)/(4D - 3^{1/2}a^{2}),
D, U, V, W as at X(1337); see Hyacinthos #8874Let A'BC be the internal equilateral triangle on side BC, and define CB'A and AC'B cyclically. Let (AB'C') be the circle passing through the points A, B', C', and define (BC'A') and (CA'B') cyclically. The three circles concur in X(1338). For details, see X(1337).
X(1338) lies on these lines: 4,617 1157,1337