Problem 23 (1986 AJHSME)

The large circle has diameter $\overline{AC}$. The two small circles have their centers on $\overline{AC}$ and just touch at $O$, the center of the large circle. If each small circle has radius $1$, what is the value of the ratio of the area of the shaded region to the area of one of the small circles? [See figure in original PDF]