Hole in Paper

A hole is cut off from a paper sheet. Can you split the sheet in two pieces, so that after rearranging them, the hole moves to the center of the square? What is the optimal way you can do it, i.e. with least amount of cutting?

Remark: You can assume you can cut with perfect accuracy.

Cut a circle with the same diameter from the center of the sheet and place it over the hole. If the two circles overlap, just make sure you rotate the cut off piece properly after placing it over the hole.