I don't like pizza crust

Geometry Level 1

Is it possible to cut a circle into pieces with these conditions?

There are finitely many pieces.
The pieces must be congruent, meaning that they have the same shape and area.
Some of the pieces have at most one point on the circumference of the circle.
Curved cuts are allowed.

This cutting is only <strong>partially</strong> correct. It satisfies all but the "same shape" condition. This cutting is only partially correct. It satisfies all but the "same shape" condition.