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too complicated to be written here. Click on the link to download a text file. 

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 #8509111215 & 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 E(262), 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. 
