Problem:
Eight semicircles line the inside of a square with side length as shown. What is the radius of the circle tangent to all of these semicircles?
Answer Choices:
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Solution:
Let be the center of the circle and choose one of the semicircles to have center point . Label the point of tangency and point as in the figure. In and , so . Because , .
The problems on this page are the property of the MAA's American Mathematics Competitions