Let $\alpha$ and $\beta$ $C^1$ boundaries of two topological disks in the plane. We can change $\alpha$ by rigid motions and homoteties to $\tilde{\alpha}$, such that $\beta$ is inside the bounded component of $\tilde{\alpha}$. The point is: "What is the minimal such $\tilde{\alpha}$?" There are lots of questions one can do about this, for example:
"Fix the minimal length of $\tilde{\alpha}$ with that property. How many solutions do we have with this length? We can see this set of solutions as a subset of $\mathbb{R}^2 \times\mathbb{S}^1$."