OSN 2002 Problem 7

Let $ABCD$ be a rhombus where $\angle DAB = 60^\circ$ , and $P$ be the intersection between $AC$ and $BD$ . Let $Q,R,S$ be three points on the boundary of $ABCD$ such that $PQRS$ is a rhombus. Prove that exactly one of $Q,R,S$ lies on one of $A,B,C,D$ .