18. The diagram shows two identical squares, $A B C D$ and $P Q R S$, overlapping each other in such a way that their edges are parallel, and a circle of radius $(2-\sqrt{2}) \mathrm{cm}$ covered within these squares. Find the length of the square $A B C D$.
18. Ans: 1 .
As the diagram below shows, $P Y=\sqrt{2} O P$ and $Y S=O P-\frac{1}{2} P Y$. Thus,
$$
P S=P Y+Y S=\frac{2+\sqrt{2}}{2} O P=\frac{2+\sqrt{2}}{2}(2-\sqrt{2})=1 .
$$