KöMaL 2018 C1500

On a line segment $AB$, the points $X$ and $Y$ are marked, and the squares $AXPQ$, $XBRS$, $BYWV$ and $YAUT$ are drawn, with their vertices labelled in counterclockwise order. The centres of the squares are denoted by $K$, $L$, $M$ and $N$, respectively. Prove that the line segments $KM$ and $LN$ are perpendicular and equal in length.