Let $C$ be a simple, compact, connected curve and $\Omega$ its inner domain. Let supose that $\Omega$ has a ball of radius $r$. Prove a inequality involving the area of $\Omega$: $A(\Omega)$ and and the length of $C$:L but L can not appear squared or having any power.
I managed to prove that in a different problem with the curve inside a ball getting $$ A(\Omega) \leq \frac{r}{2}L, $$ just by using divergence theorem. Any idea for this?