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X(1), X(3), X(4), X(32), X(39), X(76), X(83), X(194), X(384), X(695), X(2896), E(566), E(619), E(657)

excenters

vertices of cevian triangle of X(384)

vertices of the first and third Brocard triangles

K020 is the isogonal pK with pivot X(384) hence a member of the Euler pencil. See Table 27.

Locus properties :

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. This is also true with the third Brocard triangle.

In the case of the first Brocard triangle, the locus of the perspector is K322.

See a generalization at CL041.