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Problem 283: Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius.

The figure shows a circular sector AOB of 90 degrees with radius R. OB is the diameter of semicircle C. In the region between the sector AOB and the semicircle C, a circle D is inscribed, tangent to OA, arc AB, and the semicircle C. If r is the radius of the circle D, prove that r = R / 4.

Circular sector, radius 


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