Let $x$ and $y$ be points in a metric space and let $B(x,r)$ and $B(y,s)$ be usual open balls. Suppose $B(x,r)=B(y,s)$. Must $x=y$? Must $s=r$? 

What I got so far is that: $$r \neq s \implies x \neq y$$ but that's it.