GMAT Problem Solving Question 32: Circles and Equilateral triangles

 
Try the following GMAT Problem Solving question that tests your understanding of how to set up geometry problems that involve circles and equilateral triangles on the GMAT.

Question 32:

In the figure below, each of the three large circles are tangent to the other two circles, the small circle, and the two sides of the equilateral triangle. If the length of each side of the equilateral triangle is $12$, then what is the radius of the small circle?

1. $\quad 7-4\sqrt{3}$
2. $\quad 3\sqrt{3}-5$
3. $\quad 2-\sqrt{3}$
4. $\quad 9-5\sqrt{3}$
5. $\quad 6-3\sqrt{3}$