Problem:
Isosceles right triangle encloses a semicircle of area . The circle has its center on hypotenuse and is tangent to sides and . What is the area of triangle
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Answer Choices:
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Solution:
Reflect the triangle and the semicircle across the hypotenuse to obtain a circle inscribed in a square. The circle has area . The radius of a circle with area is . The side length of the square is and the area of the square is . So the area of the triangle is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions