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Problem 284: Circular Sector 90 degrees, Semicircles, Tangent, Radius

The figure shows a circular sector AOB of 90 degrees with radius R. OB is the diameter of semicircle C. Semicircle D is tangent to semicircle C and arc AB at E and A, respectively. If r is the radius of the semicircle D, prove that r = R / 3.

Circular Sector 90 degree

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