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Question

A circle with radius r is contained within the region bounded by a circle with radius R. The area bounded by the larger circle is ab times the area of the region outside the smaller circle and inside the larger circle. Then R:r equals:

Accepted Answer

The area of the larger circle is R^2, and the area of the region outside the smaller circle and inside the larger circle R^2 - r^2. Thus, R^2 = ab ( R^2 - r^2) R^2 = ab R^2 - ab r^2 ab r^2 = (ab -1)R^2 ab a-bb = R^2r^2 aa-b = R^2r^2 aa-b = Rr The answer is a:a-b.