ÖMO 2008 Problem 3

We are given a line $g$ with four successive points $P$ , $Q$ , $R$ , $S$ , reading from left to right. Describe a straightedge and compass construction yielding a square $ABCD$ such that $P$ lies on the line $AD$ , $Q$ on the line $BC$ , $R$ on the line $AB$ and $S$ on the line $CD$ .