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X(3), X(6), X(183), X(956), X(1344), X(1345) common points of the Thomson cubic and the circumcircle i.e. vertices of the Thomson triangle infinite points of pK(X6, X5640) where X5640 = X2X51 /\ X6X110 Vertices of the orthocentroidalisogonic triangle, on the cevian lines of O 

Let M be a variable point on the circumcircle. The trilinear polar of M meets the line OM at M'. The locus of M' is K297. K297 is a nodal circumcubic with node K. See the related quartic Q090. K297 is the isogonal transform of K295. K297 is a member of the pencil generated by the Thomson cubic K002 and the union of the circumcircle and the Brocard axis. This also contains K167, K172. 
