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X(1), X(6), X(57), X(58), X(81), X(222), X(284), X(1172), X(1433), X(3194)

K319 is the locus of point P whose

1. anticevian triangle is perspective to CP2, the 2nd circumperp triangle (see TCCT, §6.22),
2. circumanticevian triangle is perspective to CP2, the 2nd circumperp triangle (see TCCT, §6.22) together with the external bisectors,
3. circumanticevian triangle is perspective to TCP2, the tangential triangle of the 2nd circumperp triangle (see TCCT, §6.24).

See also table 6.

K319 is anharmonically equivalent to the Thomson cubic. See Table 21.

K319 is the isogonal transform of K345.

It is a member of the class CL043 : it meets the circumcircle at A, B, C and three other points where the tangents are concurrent at X = X(14969).