# 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 $$x + y$$ .

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