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X(523)

RaRbRc anticevian triangle of X(523)

K079 = Kp(X115)++ is a member of the class CL016 of cubics. Now, F = X(523) and Kc(X115) is the union of the perpendicular at G to the Euler line and the parabola with focus X(125) center of the Jerabek hyperbola, with directrix the Euler line. It is the complement of the Kiepert parabola. The tangents at Ra, Rb, Rc are concurrent at X(115) and bound a triangle perspective to the medial triangle. The lines ARa, BRb, CRc are parallel to L, perpendicular to the Euler line.

The equation of this particular cubic is obtained from the general equation above with (l:m:n) = (a^2:b^2:c^2).

See also CL029.