Another way of tackling the problem requires challenging the wording of the puzzle. Nothing in the wording specifies the formation of the circle. I.e., are the circles DISCS or RINGS? Answers provided thus far assume the circles are to be shaped as discs. But if they can be rings, then only one sheet of paper is needed.
If the "circles" can be rings, here's how it can be done with one sheet of paper. Rather obvious but I like to spell things out anyway:
I thought about that. But the OP states your child needs to "cut out 10 circles". Her assignment was not to "glue," "tape," "construct," or even "make" -- it was "cut out."
Although, she should still get her credit and praise for creativity, if she does not blab out that a parent has done the project for her.