A semicircle is inscribed in a semicircle of radius 2 as shown. Find the radius of the smaller semicircle.
Solution: Draw a line from the center of the smaller semicircle to the center of the larger one, and a line from the center of the larger semicircle to one of the other points of intersection of the two semicircles. We now have a right triangle whose legs are both the radius of the smaller semicircle and whose hypotenuse is 2 , therefore the radius of the smaller semicircle is $\sqrt{\mathbf{2}}$.