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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)