Problem:
A semicircle is inscribed in a semicircle of radius as shown. Find the radius of the smaller semicircle.
Solution
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 , therefore the radius of the smaller semicircle is .
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