Calculate the distance between any points in two different circles

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I have two overlapping circles (C1 and C2) for which the distance between their centers is know. Inside each circle theres's random number of points (P11... P1n and P21... P2n) for which the distance between each of them and the center of the circle is also known. Given only that information, is it possible to calculate the distance between any two P1x and P2x points?