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X(2), X(115), X(523), X(1312), X(1313), X(3413), X(3414)

where X(3413), X(3414) are the infinite points of the Kiepert hyperbola

Ma, Mb, Mc midpoints of ABC

vertices of the anticevian triangle of X(523)

K237 is a pK invariant in the Hirst transform with pole X(115) - the center of the Kiepert hyperbola - and conic the Kiepert hyperbola : for any point M on K237, the line MX(115) meets the polar line of M in the Kiepert hyperbola at M' on the cubic. Hence, K237 is a member of the class CL032 of cubics.

K237 has three real asymptotes. One is the perpendicular at G to the Euler line. The remaining two are parallel to those of the Kiepert hyperbola and meet at the midpoint of GX(115).

The tangents at A, B, C, G pass through X(115). Those at Ma, Mb, Mc, X(115) are perpendicular to the Euler line.

K237 meets the nine point circle at Ma, Mb, Mc, X(115), X(1312), X(1313) and the inscribed Steiner ellipse at Ma, Mb, Mc, X(115), S1, S2. These two latter points lie on the line GK and on the two asymptotes of the Kiepert hyperbola. The Hirst inverses of X(1312), X(1313) are T1, T2 on the orthic axis and on the circum-conic through G and K.

The Hirst inverses of Ma, Mb, Mc are the vertices of the anticevian triangle of X(523).