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K444
equK444

X(4), X(32), X(194), X(14251), X(32544), X(32545), X(32546)

Brocard points

imaginary foci of the Brocard ellipse

vertices of the cevian triangle of K

infinite points of K1027 = pK(X6, X76)

vertices of the ITB triangle : points on the circumcircle and K410

vertices of the third Brocard triangle

K444 meets the circumcircle at 6 points where the tangents concur at the Lemoine point K. See the related K579, K693, K694.

See Cubics Related to Coaxial Circles ยง10.4 and Circumcubics meeting the Circumcircle at six points with concurring tangents.

K512 is the isogonal transform of K444.

K444 is psK(X32, X6, X4) in Pseudo-Pivotal Cubics and Poristic Triangles.

See also K1101, a related stelloid, K1103, a focal cubic.

Let us recall that, for any P on K444, there is a pK with pivot P passing through the vertices of the ITB triangle and then, its isopivot lies on K1104.

Locus property

Let (H) be a rectangular hyperbola with center X(39), passing through the Brocard points. Let (H') be the rectangular circum-hyperbola with the same points at infinity. (H) and (H') meet again at two points, collinear with X(32), which lie on K444.