Bowls is a sport played on courts, which are flat and level grounds, limited by perimeter wooden boards. The objective of this sport is to throw bowls, which are balls made of synthetic material, in such a way as to place them as close as possible to the jack, which is a smaller ball made, preferably, of steel, previously thrown. Suppose that a player threw a bowl with radius 5 cm that ended up touching the jack with radius 2 cm, as illustrated in Figure 2. Consider point $C$ as the center of the bowl, and point $O$ as the center of the jack. It is known that $A$ and $B$ are the points where the bowl and the jack, respectively, touch the ground of the court, and that the distance between $A$ and $B$ is equal to $d$. Under these conditions, what is the ratio between $d$ and the radius of the jack? (A) 1 (B) $\frac{2\sqrt{10}}{5}$ (C) $\frac{\sqrt{10}}{2}$ (D) 2 (E) $\sqrt{10}$
Bowls is a sport played on courts, which are flat and level grounds, limited by perimeter wooden boards. The objective of this sport is to throw bowls, which are balls made of synthetic material, in such a way as to place them as close as possible to the jack, which is a smaller ball made, preferably, of steel, previously thrown. Suppose that a player threw a bowl with radius 5 cm that ended up touching the jack with radius 2 cm, as illustrated in Figure 2.
Consider point $C$ as the center of the bowl, and point $O$ as the center of the jack. It is known that $A$ and $B$ are the points where the bowl and the jack, respectively, touch the ground of the court, and that the distance between $A$ and $B$ is equal to $d$. Under these conditions, what is the ratio between $d$ and the radius of the jack?
(A) 1
(B) $\frac{2\sqrt{10}}{5}$
(C) $\frac{\sqrt{10}}{2}$
(D) 2
(E) $\sqrt{10}$