[1] The conic k

[2] Le point P vary on line BC and P' be the intersection of A*P with the polar s' of S with respect to k

[3] Consider the other than A* intersection point A

[4] Let A

[5] The three analogously defined conics {k

The proofs of the statements follow immediately by applying an appropriate projectivity to the corresponding configuration resulting when S obtains the position of the centroid of ABC. In that case the three conics {k

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