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X(13), X(14), X(476), X(523), X(5466), X(14559)
X = X(5466), on the asymptote
F3 = X(14559), on the Fermat line
In memoriam Igor Fedorovitch Sharygin who passed away today (March, 12 2004)
O(X523) is the orthopivotal cubic with orthopivot the point at infinity of the orthic axis. See the FG paper "Orthocorrespondence and orthopivotal cubics" in the Downloads page and Orthopivotal cubics in the glossary.
K064 is the only nK0(W,W) which is circular. It belongs to the class CL026 of cubics. The pole and the root are both X(1989).
Its singular focus is the centroid G and lies on the real asymptote, the perpendicular at G to the Euler line. It follows that K064 is a nK0+. See CL044.
The tangents at A, B, C are the sidelines of the antimedial triangle and the cubic is tritangent at those points to the Steiner ellipse.
Compare K064 with K024, the only equilateral nK0(W,W) and with K278 = pK(X1989, X1989).
The isogonal transform of K064 is K148.