IMO 1985 LL ITA46

Let C be the curve determined by the equation y = x3 in the

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IMO 1985 LL ITA46

Origin: ITA

Problem

Let C be the curve determined by the equation y = x3 in the rectangular coordinate system. Let t be the tangent to C at a point P of C; t intersects C at another point Q. Find the equation of the set L of the midpoints M of PQ as P describes C. Is the correspondence associating P and M a bijection of C on L? Find a similarity that transforms C into L.