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X(1), X(4), X(30), X(125), X(140), X(3574) excenters A', B', C' vertices of the orthic triangle infinite points of K005 green points described below 

Denote by Ap, Bp, Cp the pedal triangle of P. The Euler lines of triangles – PBpCp, PCpAp, PApBp concur (at Q) if and only if P lies on the Neuberg cubic (together with the line at infinity), – ABpCp, BCpAp, CApBp concur (at Q) if and only if P lies on the Napoleon cubic (together with the line at infinity). In both cases, the locus of Q is the circular sextic Q093 with focus X(113). H is a quadruple point on the curve and the three tangents at H are parallel to the asymptotes of K003. Each tangent at H meets Q093 at H (four times) and at another double point which also lies
These three double points are represented in green on the figure. Q093 is tangent at the in/excenters to K003 thus the tangents at these points pass through O. 
