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X(3), X(4), X(54), X(1342), X(1343), E(664) vertices of the circumnormal triangle infinite points of the Napoleon cubic K005 see below for more details and also Table 25 

The McCay cubic K003 and the Lemoine cubic K009 are two circumcubics passing through O, H and the vertices of the circumnormal triangle. Both cubics meet the sidelines of ABC at three points which are the vertices of a cevian triangle (that of O for K003 and that of G for K009). These two cubics generate a pencil of cubics which contains a third cubic with the same properties and this cubic is K361. K361 is the isogonal transform of K026, the (first) Musselman cubic or KN++. Recall that the Lemoine cubic K009 is the isogonal transform of K028, the (third) Musselman cubic. K361 is also psK(X54, X95, X3) in PseudoPivotal Cubics and Poristic Triangles and spK(X5, X140) in CL055. See also Table 54 where K361 is mentioned in one line and three columns showing that it belongs to four pencils of cubics generated by : • pK(X6, X140) and K187, line Q = X140, • K002 and K028, column P = aQ, • K003 and the union of the Euler line with the circumcircle, column P = [X3], already mentioned above, • K006 and K080, column P = S. *** K361 contains :
*** Locus properties : 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 loci of the poles and isopivots of such cubics are K378 and K405 respectively.

