Geometry : Circles touching externally

Problem : 17 ) 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 a radius of 1 unit and passes through the center of circle D. Find the radius of circle B.

Solution : 

Radius (r) = 8/9 units.

here is the diagram in the link given below.
http://i854.photobucket.com/albums/ab104…

Note :
If two circles touch each other externally or internally then, the point of contact and the centers of the touching circles will be COLLINEAR.

Further, since the radius of circle A is 1 unit and it passes through the center of the bigger circle, therefore the radius of the bigger circle will be 2 units and hence DB = (2 - r).


Link to Y/A