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see the general equation of Kw(P) in CL017.

X(53), X(216), X(264), X(393), X(1249)

midpoints of ABC

K208 = Kw(X4) is the locus of poles of pK+ with pivot X(4). It is a member of the class CL017 of cubics.

The locus of the point of concurrence of the asymptotes is K412 = Kc'(X4). See CL018.

For example :

  • pK+(X393, X4) is the union of the altitudes,
  • pK+(X53, X4) = K049 is an equilateral cubic, the McCay cubic of the orthic triangle.
  • pK+(X216, X4) = K044 is a pK++ with center X(5), the Darboux cubic of the orthic triangle.
  • pK+(X1249, X4) = K329 contains the four CPCC points, see table11.

See also the class CL019 of pivotal cubics with pivot H.

K208 is also psK(X14569, X2, X53) in Pseudo-Pivotal Cubics and Poristic Triangles.

See also K207 = Kw(X1).