BD-BDMO 2022 Problem 5

In an acute triangle $\triangle ABC$ , the midpoint of $BC$ is $M$ . Perpendicular lines $BE$ and $CF$ are drawn respectively on $AC$ from $B$ and on $AB$ from $C$ such that $E$ and $F$ lie on $AC$ and $AB$ respectively. The midpoint of $EF$ is $N.$ $MN$ intersects $AB$ at $K.$ Prove that, the four points $B,K,E,M$ lie on the same circle.