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?[asy]
size(200);
defaultpen(linewidth(0.8));defaultpen(fontsize(8));
draw(Circle(origin, 2));
draw(Circle((-1,0), 1));
draw(Circle((6/9, 8/9), 8/9));
draw(Circle((6/9, -8/9), 8/9));
label("A", (-1.2, -0.2), NE);
label("B", (6/9, 7/9), N);
label("C", (6/9, -7/9), S);
label("D", 2*dir(110), dir(110));[/asy]<spanclass=′latex−bold′>(A)</span>32<spanclass=′latex−bold′>(B)</span>23<spanclass=′latex−bold′>(C)</span>87<spanclass=′latex−bold′>(D)</span>98<spanclass=′latex−bold′>(E)</span>31+3