How do you divide a circle into a certain number of shapes with the same area while having at least one sub circle dividing the whole figure? I know that if we divide along the center of the circle in even angles the shapes cut are the same in size so therefore their area would be the same.

What I want is something along the lines of this:

where a subcircle of any radious is present inside but the pieces of it still have the same area as the pieces outside.