Here's how I would approach it (thehardway- someone cleverer may be able to find a simpler way):

Start by setting up a coordinate system such that the origin is at the bottom of the large (radius 3) circle and the y axis is a diameter. Then that circle has equation or . The next circle, with radius 2, is tangent to that first circle at (0, 6) and so must have center at (0, 4) and equation . Finally, the circle with radius 1 has center at (0, 1) and so equation .

In terms of that coordinate system, the problem is to find a, b, and r so that is tangent to all three of those circles.