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angle chasing related to circle inscribed in square

Source: 2019 Oral Moscow Geometry Olympiad grades 10-11 p1

May 22, 2019
geometrysquareincircleangle

Problem Statement

Circle inscribed in square ABCDABCD , is tangent to sides ABAB and CDCD at points MM and KK respectively. Line BKBK intersects this circle at the point L,XL, X is the midpoint of KLKL. Find the angle ∠MXK\angle MXK .
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