Yin Yang

Geometry Level 3

Diameter ACE is divided at C in the ratio 2:3 The two semicircles, ABC and CDE, divide the circular region into an upper (shaded) region and a lower region. The ratio of the area of the upper region to that of the lower region can be expressed as\(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b \)?

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