Problem of the Day #103

POTD March 21, 2024

Let ABCDEF be a regular hexagon with side length 2. A circle with radius 3 and center at A is drawn. The area inside quadrilateral BCDE but outside the circle can be written as \sqrt a - \frac{b}{c} \pi, where a,b,c are positive integers with b and c relatively prime. Find a+b+c.