A circle is inscribed in a square. The square is inscribed in another circle. What is the ratio of the area of the smaller circle to the area of the larger circle?
Correct: D
Let the side of the square be s. The radius of the smaller circle is s/2, and its area is pi*(s/2)^2 = pi*s^2/4. The diagonal of the square is s*sqrt(2). The radius of the larger circle is (s*sqrt(2))/2, and its area is pi*((s*sqrt(2))/2)^2 = pi*s^2/2. The ratio of the smaller area to the larger area is (pi*s^2/4) / (pi*s^2/2) = (1/4) / (1/2) = 1/2.