14) Seven circles of unit radius are arranged as shown in the figure below. The distance between the two centers indicated by a dot is

(A) 2

(B) $\sqrt{3}$

(C) 3

(D) $2 \sqrt{3}$

(E) none of the above.

![](https://cdn.mathpix.com/cropped/2024_04_17_241a8f7ac8d78bebac61g-2.jpg?height=246&width=272&top_left_y=548&top_left_x=1184)
14) The answer is $(D)$.

The centers of the external circles are the vertices of a regular hexagon with side length 2 in triangle $A B C$, the angle $A \hat{B} C$ is $60^{\circ}$, so $A C=\frac{\sqrt{3}}{2} \cdot 2$.

![](https://cdn.mathpix.com/cropped/2024_04_17_f4c23f6ec499ad3e7a1fg-2.jpg?height=294&width=322&top_left_y=2057&top_left_x=1615)