Question 23Circles $A,$ $B,$ 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 $B?$ $\dfrac{2}{3}$$\dfrac{\sqrt{3}}{2}$$\dfrac{7}{8}$$\dfrac{8}{9}$$\dfrac{1 + \sqrt{3}}{3}$
