MathDB
Three half-circles - find the length of AB

Source: Baltic Way 1996 Q2

July 12, 2011
geometrygeometry proposed

Problem Statement

In the figure below, you see three half-circles. The circle CC is tangent to two of the half-circles and to the line PQPQ perpendicular to the diameter ABAB. The area of the shaded region is 39π39\pi, and the area of the circle CC is 9π9\pi. Find the length of the diameter ABAB.
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