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A, B, C, H which are triple

X(74), X(671), X(895), X(1156), X(1320),

A', B', C' reflections of A, B, C in the sidelines

Q001 is a bicircular septic which solves the Darboux problem. See K172.

It is the antigonal image of the Lucas cubic. (see Hyacinthos #8509-11-12-15 & sq.) and the isogonal transform of Q071.

It has three real asymptotes parallel to those of the Lucas cubic or the Thomson cubic.

The "last" point on BC is [0 : a^2 + 3(b^2 - c^2) : a^2 - 3(b^2 - c^2)], the other points on CA, AB similarly. These points are the vertices of the pedal triangle of X(3146), the homothetic of H under h(O,3).

The tangents at A, B, C are the symmedians and the two other tangents at each vertex are not always real.