Open Cover of $0 < |x| \leq 1$ in $\mathbb{R}$?

I have to give an example of the following:

Let $A = \{x \in \mathbb{R^2} \ |\ 0 < |x| \leq 1\}$. Give an open cover of $A$ that has no finite subcover of $A$.

Furthermore, I have to prove this is true, but I cannot think of an example. I know an example of such a problem for the interval $(0,1)$ in $\mathbb{R}$, but I cannot think of one for this problem. Any help is greatly appreciated!