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2) Given a Euclidean circle q in u, is there a map f : u → u that is both a Euclidean rigid motion and a hyperbolic rigid motion that takes q to q? Use the last homework problem in homework #6 and symmetry to prove that the hyperbolic and Euclidean centers of q lie on the same vertical line. (You are allowed to assume that q is also a hyperbolic circle.)Please explain each step

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