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X(1), X(2), X(6), X(597)


cevians of X(597)

K282 is the isogonal pK with pivot X(597), the midpoint of GK. It is a member of the Thomson-Grebe pencil. See Table 13.

It has nine known common points with K018 (second Brocard cubic) which are A, B, C, G, K (these two double) and the two imaginary foci of the Lemoine ellipse, the in-ellipse with (real) foci G and K. The tangents at G, K to both cubics pass through X(111), the singular focus of K018.

K018 and K282 generate a pencil of cubics which contains K280, K281, K283, K284.