There is a circle area with radius 1 km. And there is a tunnel, which is just under the surface, but invisible, unless you dig. It is known that the tunnel goes under the area (at least touches it at one point), it is straight and infinitely long (in both directions).
You have a plow and can dig along a lines with it. When you plow and cross the tunnel you find it. How much (how long) and where you have to plow to guarantee that you find the tunnel?
You are allowed to plow outside of the area as well as inside. You can take plow out of the ground and move over the ground without plowing.

For example, you can chose to plow just along the perimeter, then you result would be 2*pi=6.43 km. The task is to make this number as small as possible.

I don't know any good approach, but two people told me that at least 4.83km is possible to achieve.