Problem:
The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle?
Answer Choices:
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Solution:
Let the triangle have vertices , and , let be the center of the circle, and let be the midpoint of . Triangle is a degree triangle. If is the radius of the circle, then the sides of are , and . The perimeter of is , and the area of the circle is . Thus , and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions