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SHARYGIN 2012 Problem 19

    Two circles with radii 1 meet in points X,YX, Y , and the distance between these points also is equal to 11 . Point CC lies on the first circle, and lines CA,CBCA, CB are tangents to the second one. These tangents meet the first circle for the second time in points B′,A′B', A' . Lines AA′AA' and BB′BB' meet in point ZZ . Find angle XZYXZY .

    Dataset text AI-MO AoPS. Quoted with source.

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