Problem:
A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square with sides of length . What is the length of each side of the octagon?
Answer Choices:
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Solution:
Let represent the length of each side of the octagon, which is also the length of the hypotenuse of each of the right triangles. Each leg of the right triangles has length , so
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions