Free GRE Practice Question

A square has side length \(4\). Two congruent larger semicircles are drawn inside the square with their diameters lying along two opposite sides of the square, so each larger semicircle has radius \(2\); these two semicircles meet at the center of the square. A third, smaller semicircle is drawn inside the square with its diameter along one of the remaining two sides, centered at the midpoint of that side, and it is tangent to both larger semicircles. What is the diameter of the smaller semicircle?