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X(2), X(2394) → X(2419), X(30508), X(30509), X(50941), X(50942), X(50943), X(50944), X(50945), X(57455) → X(57460) 

The Simson cubic is the locus of tripoles of the Simson lines of triangle ABC hence it is the dual of the Steiner deltoid H3. A study can be found at : http://forumgeom.fau.edu/FG2001volume1/FG200115index.html The Simson cubic is a special case of isotomic conicopivotal isocubic. It is cK(#X2, X69). The line PQ (see below) envelopes the ellipse centered at K which is inscribed in the antimedial triangle. The contact conic is the circumconic centered at X(216). The three real inflexion points lie on the trilinear polar of X(95). See Special isocubics, §8. The isogonal transform of the Simson cubic is K162 = cK(#X6, X3) and its Hisoconjugate is K406. The homothetic of K010 under h(G,1/4) is related to the class CL001 of isogonal central nK cubics. The Trilinear Centroidal Conjugate of K010 is K408. See definition and properties at CL045. Locus properties :

