OIM 2018 Problem 6

Let $ABC$ be an acute triangle with $AC > AB > BC$ . The perpendicular bisectors of $AC$ and $AB$ cut line $BC$ at $D$ and $E$ respectively. Let $P$ and $Q$ be points on lines $AC$ and $AB$ respectively, both different from $A$ , such that $AB = BP$ and $AC = CQ$ , and let $K$ be the intersection of lines $EP$ and $DQ$ . Let $M$ be the midpoint of $BC$ . Show that $\angle DKA = \angle EKM$ .