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Two circles and tangents

Source: Sharygin Geometry Olympiad 2012 - Problem 19

April 28, 2012
geometry3D geometryprismprojective geometryincentergeometric transformationdilation

Problem Statement

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.
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