## X(2144) (X(2)-EIGENTRANSFORM OF X(238))

 Interactive Applet

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 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)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.