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X(3), X(4), X(54), X(140), X(1493) midpoints of ABC infinite points of the Napoleon cubic K005 points of pK(X6, X140) on the circumcircle 

K569 is a cubic related to circular psK cubics with pseudopivot G. See PseudoPivotal Cubics and Poristic Triangles. Its isogonal transform is K849 = spK(X140, X3628). It is a member of the pencil generated by K002 and K009. See Table 50. It is also a member of the pencil generated by K005 and the union of the line at infinity with the Jerabek hyperbola. All these cubics are spK(X5, Q) with Q on the Euler line as in CL055. Apart K005, this pencil contains two psKs which are K569 = spK(X5, X3628) and K361 = spK(X5, X140) = psK(X54, X95, X3). The central cubic K566 = spK(X5, X548) is another remarkable member. 
