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K917

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X(4), X(3522)

infinite points of K832 = pK(X6, X631)

points on (O) of pK(X6, X11439)

three common points of the line (L) = X(3)X(1495) and pK(X6, X11439)

Geometric properties :

K917 is the locus of Q such that spK(cQ, Q) has three concurring asymptotes (at X). See K525 and CL066. The locus of X is K028.

K917 is a nodal circum-cubic. The node is H with nodal tangents parallel to the asymptotes of the Jerabek hyperbola.

K917 belongs to the pencil generated by the third Musselman cubic K028 and the union of the altitudes of ABC.

Locus property :

Let M be a variable point on the circumcircle and let S(M) be the Steiner line of M. S(M) and the line MX(3522) meet at N on K917. See Table 43 for a generalization and other examples.