2009 AMC 10B Problem 16

Points A and C lie on a circle centered at O, each of \overline{BA} and \overline{BC} are tangent to the circle, and \triangle ABC is equilateral. The circle intersects \overline{BO} at D. What is \frac{BD}{BO}?

\text{(A) } \frac {\sqrt2}{3} \qquad \text{(B) } \frac {1}{2} \qquad \text{(C) } \frac {\sqrt3}{3} \qquad \text{(D) } \frac {\sqrt2}{2} \qquad \text{(E) } \frac {\sqrt3}{2}

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