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 $DCA$ (Proposed by M.Volchkevich)
Source: Sharygin Geometry Olympiad Correspondence round 2016 P-5 Grade-8
Tags: geometry
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 $DCA$ (Proposed by M.Volchkevich)