You own a square-shaped table. You want to drill a small hole in the center to place an umbrella stand. Unfortunately, you're a little drunk:
Alas. Fortunately, not all is lost. You are sober now, and have a hacksaw.
(a) Cut the table into two pieces. Reassemble them to make a square-shaped table the same size as the original, but with the circular hole in the exact center. The cut does not have to be a straight line, but it must divide the table into exactly two pieces.
(b) Now, minimize the length of the cut.
In this puzzle, everything is 2D. No tricky 3D cuts. Note added in later, after people started rightly questioning what a hacksaw can do: Don't worry about what cuts are physically possible with a hacksaw. Any division of the table into two pieces is allowed.
WARNING: When I give this puzzle to people, about 10% of them see the solution right away, about 30% figure out part (a) quickly and then spend varying amounts of time on part (b), and the other 60% give up. If you scroll down and look at the comments or answers, you will have robbed yourself of a deep 'aha!' moment.