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X(74), X(133), X(1511), X(3163)

midpoints A', B', C' of ABC

other points below

K564 is a psK parent of the Thomson cubic K002. As such, it contains the midpoints of ABC and the tangents at A, B, C are the symmedians.

It meets the circumcircle again at X(74) and two other points Q2, Q3 on the tangent at X(3163) to the Steiner inscribed ellipse.

It meets the Steiner inscribed ellipse at A', B', C', X(3163) and two other points R2, R3 on the polar line of X(74) in this ellipse.

The tangents at X(74), Q2, Q3 are concurrent.

See Pseudo-Pivotal Cubics and Poristic Triangles.