



 
Ray, Are you sure you have worded the problem correctly? Look at Stephen's response to a similar question. Penny Ray wrote back
Ray, You can't determine the area of either circle just the area of the annulus between the circle, the region shaded light purple in Stephen's diagram. To convince yourself draw a line segment $AB$ with a given length and let $M$ be the midpoint of $AB.$ Draw a line $l$ through $M,$ perpendicular to $AB$ and let $C$ be any point in $l.$ Draw a circle with centre $C$ and radius $MC$ and another circle with centre $C$ and radius $CA.$ Now select a different point $C$ on $l$ and repeat the construction. In the two diagrams the two small circles and the two large circles have quite different areas and yet, as Stephen showed, the regions between the two circles are equal in area. Penny
 


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