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X(2), X(6), X(7), X(13), X(14), X(673), X(694)

extraversions of X(7), X(673), X(694)

points at infinity of the Steiner ellipse and the Thomson cubic

midpoints of ABC with tangents passing through K

intersections of the axes of the Steiner ellipse and the circumcircle

intersections of the Steiner ellipse and the line GK

6 points on the symmedians: (±bc,b^2,c^2), (a^2,±ac,c^2), (a^2,b^2,±ab)

Q012 is a circum-quintic with four nodes namely A, B, C, G.

The nodal tangents at A, B, C are the corresponding internal and external bisectors. The nodal tangents at G are the axes of the Steiner ellipse.

Q012 has three real asymptotes parallel to those of the Thomson cubic and concurring at K. It has also two imaginary asymptotes secant at X(599).

Locus properties :

  • locus of F such that the Stothers cubic ST(F) has rectangular nodal tangents. See CL030.
  • locus of point M such that the circum-conic and inconic with same perspector M have parallel axes, or equivalently such that the pencil of conics generated by these two conics contains a circle. See K002, property 22 for related topics.
  • locus of node N of nodal circum-cubics passing though G and having asymptotes parallel to those of the Thomson cubic K002. See K281, K295 for instance.

See a generalization in Table 28 : cevian and anticevian points and also Cax(F) in CL047.

The isogonal transform of Q012 is Q090.