This question already has an answer here:
- Find a straight tunnel 8 answers
Consider a unit circle C. The goal is to find a curve L such that:
- all secant lines of C intersect L;
- the length of L is minimal among those with property 1 above.
Any closed curve containing C (for example a circle with the same center as C, but larger) clearly satisfies property 1, but is not minimal.
The curve L does not need to be connected.
A proof of minimality of the length of L is required.