2018 OIM Problems/Problem 6

Problem

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