Figure description: An equilateral triangle encloses the two circles touching each other externally. Two sides act as common tangent to both the circles, whereas the third side is tangent to the larger circle only.
What will be the ratio of the perimeter of the smaller circle to that of the equilateral triangle in the given figure?

A

$$\pi : 12\sqrt{3}$$

B

$$\pi : 18\sqrt{3}$$

C

$$\pi : 9\sqrt{3}$$

D

$$\pi : 6\sqrt{3}$$