Problem: A circle is inscribed in an equilateral triangle, and a square is inscribed in the circle. The ratio of the area of the triangle to the area of the square is:
Answer Choices:
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Solution:
Let , respectively, represent the magnitudes of a side of the equilateral triangle, a side of the square, and a radius of the circle. Since and , the area of the triangle is and the area of the square is . The required ratio is, therefore, .