KöMaL 2005 B3837

Let $P$ and $Q$, respectively, denote the centres of the squares ABDE and BCGH drawn on the sides $AB$ and $BC$ of the triangle ABC outwards. The midpoints of the sides $AC$ and $DH$ are $R$ and $S$, respectively. Show that the points $P$, $Q$, $R$ and $S$are the vertices of a square. ( 4 points )