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X(1), X(2), X(6), X(32), X(76), X(98), X(385), X(511), X(694), X(1423), X(2319), X(3186)

Infinite points of the Steiner ellipses

See Clark Kimberling, Cubics Associated with Triangles of Equal Areas, Forum Geometricorum, vol.1, pp.161-171, 2000.

See also K354, K355 and CL041.

K128 is a member of the Thomson-Grebe pencil. See Table 13.

It is a Kiepert AntiCevian Mate of K020. See Table 32.

It is a cubic anharmonically equivalent to K020 as in Table 66.

The isotomic transform of K128 is K738 and its G-Hirst transform is K739.

The symbolic substitution SS{a -> √a} transforms K128 into K323.

Locus properties :

1. The 1st Neuberg triangle and the anticevian triangle of M are perspective if and only if M lies on K128. The locus of the perspector is K422. See the related K423.
2. The 1st (or 3rd) Brocard triangle and the anticevian triangle of M are perspective if and only if M lies on K128 and then the perspector lies on K020.
3. See another property here (in Spanish, 2017-11-19, Angel Montesdeoca).