2006 AIME II Problem 12

Equilateral \triangle ABC is inscribed in a circle of radius 2. Extend \overline{AB} through B to point D so that AD=13, and extend \overline{AC} through C to point E so that AE = 11. Through D, draw a line l_1 parallel to \overline{AE}, and through E, draw a line l_2 parallel to \overline{AD}. Let F be the intersection of l_1 and l_2. Let G be the point on the circle that is collinear with A and F and distinct from A. Given that the area of \triangle CBG can be expressed in the form \frac{p\sqrt{q}}{r}, where p, q, and r are positive integers, p and r are relatively prime, and q is not divisible by the square of any prime, find p+q+r.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.