Find the length of side AB in triangle ABC, given that the radius of the circumcircle is $$4\sqrt{3}$$ and the triangle is equilateral.

Here's how to find the length of side AB: Since triangle ABC is equilateral, all its sides are equal, and all its angles are 60 degrees. The radius of the circumcircle is given as $$4\sqrt{3}$$. We can use the formula relating the side of an equilateral triangle to the radius of its circumcircle: $$R = \frac{a}{ \sqrt{3}}$$ where R is the radius of the circumcircle and a is the side of the equilateral triangle. We are given $$R = 4\sqrt{3}$$. We need to find 'a'. $$4\sqrt{3} = \frac{a}{\sqrt{3}}$$ Multiply both sides by $$\sqrt{3}$$: $$a = 4\sqrt{3} \cdot \sqrt{3} = 4 \cdot 3 = 12$$ So, the length of side AB is 12. Answer: 12