(a) Consider a rectangular hyperbola H and a circle C intersecting H at four points P, Q, R and S. Le O and Oc denote the centers of H and C respectively. If X is the mean-point of P, Q, R, S, and is the mid-point of O and Oc, find the length XY in terms of the appropriate parameters. (b) Five points are selected on a circle of radius r. Consider the centers of the five rectangular hyperbola

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