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Tags: geometry, circumcircle, incenter, geometry unsolved



Let w be a circle and AB a line not intersecting w. Given a point P0 on w, define the sequence P0,P1, as follows: Pn+1 is the second intersection with w of the line passing through B and the second intersection of the line APn with w. Prove that for a positive integer k, if P0=Pk for some choice of P0, then P0=Pk for any choice of P0. Gheorge Eckstein