X(1), X(2), X(8), X(40), X(57), X(144), X(189), X(366), X(3062)
vertices of the cevian triangle of X(8), the Nagel point
vertices of the anticevian triangle of X(366)
points at infinity of the Thomson cubic.
K308 is the locus of point P such that the trilinear polar of P is perpendicular to the line PX(40). See CL040 for a generalization.
The isogonal transform of K308 is K760 = pK(X31, X9) and its isotomic transform is pK(X75, X312).