Divide circle and subcircle evenly by area

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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.

Circles divided by center

What I want is something along the lines of this:

Circles with subcircles divided

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