SHARYGIN 2016 Problem 5

In quadrilateral $ABCD$ $AB = CD$ , $M$ and $K$ are the midpoints of $BC$ and $AD$ . Prove that the angle between $MK$ and $AC$ is equal to the half-sum of angles $BAC$ and $DCA$ .

Official text Sharygin Geometry Olympiad 2016 official paper, page 2. Quoted with source.

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