Suppose $\alpha$ is a Jordan curve. Suppose $\beta$ is another Jordan curve such that $\alpha$ is contained in the region limited by $\beta$.
Maybe it is an easy question, but, how can one show that the length of $\beta$ is bigger than or equal to the length of $\alpha$?
Is the length of $\beta$ equal to length of $\alpha$ if and only if $\alpha=\beta$?
Thanks