Let $D_{n}$ be a set of discs. Where $n=1,2,...,n'$.
Each disc is defined as follows $D_{n}=\{(x,y)\in\mathbb{R}^{2}:(x-a_{n})^2+(y-b_{n})^2\le C^2\}$
Where $\{a_{n}\}$ and $\{b_{n}\}$ are some sets of real numbers. $C$ is constant.
Find the curve, such has the shorthest length among all curves that crosses all discs.
I know it is a general question, but i would like to know how to apply calculus of variations in order to solve this problem.
Regards.