   too complicated to be written here. Click on the link to download a text file.  X(3), X(4), X(5), X(1173), X(1487) infinite points of pK(X6, X140) points of K005 on (O)    K849 is the isogonal transform of K569 and spK(X140, X3628) as in CL055. It is also psK(X1173, X1173 x X76, X3) hence the pseudo-isopivot is X(6). It follows that the tangents at A, B, C are the symmedians. The tangents at Q1, Q2, Q3 are also concurrent at X = X(14926) on the line X(381), X(1350). Hence K849 is also a psK with respect to the triangle Q1Q2Q3. K849 is a member of the pencil generated by K005 and the union of the Euler line and the circumcircle (O). All these cubics are spK(P, Q) where P is a point on the Euler line and Q the midpoint of X5, P. See K026 (P = X3), K848 (P = X20) and obviously K005 (P = X5). The isogonal transform of every spK(P, Q) as above is spK(X5, Q), a member of the pencil generated by K005 and the union of the line at infinity and the Jerabek hyperbola. See K361, K566 for instance. 