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) is as indicated below
Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)Suppose U = u : v : w and P = p : q : r are triangle centers. The P-eigentransform of U, denoted by ET(U,P), is the point given by first trilinear
qrvw(pqu2v2 + pru2w2 - qrv2w2). Thus, ET(U) = ET(U,X(1)), and, extending the on-cubic property, ET(U,P) lies on the cubic Z(U,P) given by
upx(qy2 - rz2) + vqy(rz2 - pu2) + wrz(px2 - qv2) = 0. X(2144) lies on the 2nd equal-areas cubic, Z(X(238),X(2)) and these lines: 1,2111 2,2113 6,2109 238,2145 2053,2115 2054,2107
X(2144) = X(238)-Ceva conjugate of X(292)