Semicircles

Geometry Level 3

AB is a line segment and M is its midpoint. Semicircles are drawn with AB , AM and MB as diameters on the same side of line AB. A circle with center O is drawn which touches the three semicircles, then the radius of the smallest cicle is equal to \( \frac{ x AB }{y} \).

Find \( x + y \) .

This problem is a part of the sets - 1's & 2's & " G " for geometry.
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