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X(2), X(3)

vertices of the CircumTangential triangle and its midpoints

vertices of the Thomson triangle

foci of the Steiner in-ellipse

fixed points of the involution f in page K024

infinite points of pK(X6, X3534)

anti-points, see Table 77

K727 is pkT(X3) as defined in the page K024.

The Thomson isogonal transform of K727 is K833. See there for further properties, also Table 81 for general properties.

K1249 is an analogous cubic.