# Proof of parallel chord theorem

Where can i find a correct proof of the following theorem of H.Hopf:

For every continuous curve $L$ in the plane with endpoints $A$ and $B$ such that distance $\vert AB \vert = 1$, and for any natural number $n$, there exists a chord (meaning a straight segment with endpoints on $L$) that is parallel to $AB$ and whose length equals $1/n$.

• I can't find the proof, but it is in "H. Hopf, Uber die Sehen ebener Kontinuen und die Schleifen geschlossener Wege, Commentarii Mathematici Helvetici IX (1936-37), 303-319". If I remember correctly. – S.C.B. Feb 15 '17 at 17:18
• Very similar to this question. – Arthur Feb 15 '17 at 17:22