TITLE: Curve of length $L=1$ contained in a semicircle of diameter $2R=1$.
QUESTION [12 upvotes]: How prove  that for any curve $\alpha(s)$ of length $L=1$ in the real plane, there is a semicircle of diameter $2R=1$ that contains it.

Any hints would be appreciated.

REPLY [4 votes]: I gave up, googled and found an extremely elegant agrument (due to A. Meir) here. I guess the hard part was to locate the center of the semicircle.