Sides \overline{A B} and \overline{A C} of equilateral triangle A B C are tangent to a circle at points B and C, respectively. What fraction of the area of \triangle A B C lies outside the circle?
Answer Choices
A. \dfrac{4 \sqrt{3} \pi}{27}-\dfrac{1}{3}
B. \dfrac{\sqrt{3}}{2}-\dfrac{\pi}{8}
C. \dfrac{1}{2}
D. \sqrt{3}-\dfrac{2 \sqrt{3} \pi}{9}
E. \dfrac{4}{3}-\dfrac{4 \sqrt{3} \pi}{27}