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

X(1), X(3), X(40) Ia, Ib, Ic vertices of excentral triangle and their reflections in O i.e. the vertices of the hexyl triangle points at infinity of the McCay cubic antipodes of A, B, C on the circumcircle foci of the inconic with center O, perspector X(69) 

Q010 is the isogonal conjugate of Q009. It is a very nice central circular quintic with center O. It has three real concurring asymptotes which are the altitudes of the circumnormal triangle. The tangents at A, B, C (and at their antipodes) pass through O. The tangents at the in/excenters (and at their reflections in O) pass through H. The inflexional tangent at O passes through X(54), the Kosnita point. 
