A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. What is the ratio of the area of the smaller circle to the area of the larger square?
Answer Choices
A. \dfrac{\pi}{16}
B. \dfrac{\pi}{8}
C. \dfrac{3 \pi}{16}
D. \dfrac{\pi}{4}
E. \dfrac{\pi}{2}