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 a1/2(b1/2/v + c1/2/w - a1/2/u) : b1/2(c1/2/w + a1/2/u - b1/2/v) : c1/2(a1/2/u + b1/2/v - c1/2/w),
where u : v : w = a2 - bc : b2 - ca : c2 - abBarycentrics a3/2(b1/2/v + c1/2/w - a1/2/u) : b3/2(c1/2/w + a1/2/u - b1/2/v) : c3/2(a1/2/u + b1/2/v - c1/2/w)
X(2146) lies on the 2nd equal-areas cubic and these lines: 1,2119 238,2147 292,365 2111,2118
X(2146) = X(238)-Ceva conjugate of X(365)