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X(6)

X(324)*, X(343)* : isogonal conjugates of X(324), X(343)

vertices of the cevian triangle of X(54)

P1 : isogonal conjugate of the barycentric quotient of X(20) and O

K361 is the locus of the pivots of circumnormal pKs i.e. pKs passing through the vertices of the circumnormal triangle. With X(3), we obtain the McCay cubic and with X(54), the cubic is K373. See also Table 25.

The locus of the poles of such cubics is K378 and the locus of their isopivots is K405.

K378 is tangent at A, B, C to the cevians of X(32). The polar conic of X(32) is the circum-conic through G and K, passing through X(343)*.

K is a flex on the cubic and the inflexional tangent is the Brocard axis.

K378 is also psK(X32 x X54, X54, X6) in Pseudo-Pivotal Cubics and Poristic Triangles.