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X(4), X(32), X(194)

Brocard points

vertices of the cevian triangle of K

infinite points of pK(X6, X76)

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