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X(2), X(76), X(141), X(257), X(297), X(335), X(384), X(385), X(694), X(698), X(1916), X(2998)

X = X(14970) = isotomic conjugate of X(732)

infinite points of the Steiner ellipse

Let A1B1C1 be the first Brocard triangle and M a variable point. The lines MA1, MB1, MC1 meet BC, CA, AB at Ma, Mb, Mc respectively. These three points are collinear if and only if M lies on K017. They form a triangle perspective to ABC if and only if M lies on K020. In this case, the locus of the perspector is K322.

In other words, K322 is the locus of P whose cevian triangle is perspective to the first Brocard triangle with perspector on K020. See the related K531, K532, K533.

K322 meets the line at infinity at X(698) and the infinite points of the Steiner ellipse hence K322 has only one real asymptote. The "last" common point with the Steiner ellipse is the isotomic conjugate of X(732).

K322 is the isotomic transform of K739 = pK(X385, X6), the isogonal transform of K788 = pK(X385 x X32, X32) and the G-Hirst inverse of K354 = pK(X694, X1916).

See a generalization at CL041.

K322 is a cubic anharmonically equivalent to K020 as in Table 66.

K421 and K322 are the Kiepert Cevian Mates of the Brocard (fourth) cubic K020. See explanations in Table 32.