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K849

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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.