Circles A, B, and C are externally tangent to each other and internally tangent to circle D. Circles B and C are congruent. Circle A has radius 1 and passes through the center of D. What is the radius of circle B ?
Answer Choices
A. \dfrac{2}{3}
B. \dfrac{\sqrt{3}}{2}
C. \dfrac{7}{8}
D. \dfrac{8}{9}
E. \dfrac{1+\sqrt{3}}{3}