A closed, planar curve $C$ is said to have constant breadth $\mu$ if the distance between parallel tangent lines to $C$ is always $\mu$. $C$ needn’t be a circle. See the Wankel engine design.
b) Prove that the sum of reciprocals of the curvature at opposite points is equal to $\mu$.
c) (easy application) Prove (using b) ) that the circle of radius $R$ has constant curvature $\frac{1}{R}$.
d) Prove that the length of $C$ is $\pi\mu$.