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X(3), X(15), X(16), X(74), X(10419), X(13754)

K114 is the inversible pK with pivot X(74) and pole X(18877), the barycentric product X(3) x X(74). It is a circular cubic with singular focus X(13558), the inverse of X(125) in the circumcircle. See Special isocubics §4.4.3 and also Inverses of Isocubics.

K114 is a member of the class CL032 of cubics. The isogonal transform of K114 is K059.

It belongs to the pencil of cubics generated by the Neuberg cubic K001 and the Ki cubic K073.

K114 and the cubic which is the union of the circumcircle and the line through X(3) and X(64) generate a pencil of circular cubics stable under the inversion in the circumcircle. Their singular foci lie on the circle passing through X(3), X(74), X(107), X(186). This pencil contains K187 and K1394 which are inverse of each other.