(If you’re confused, just note that the smaller circles both touch the larger cicle in exactly one point, touch each other in exactly one point, and touch the line PQ in exactly one point. This makes the 3 centers of the circles line up.)
Talwalkar goes on to (excellently) solve this puzzle, using a and b as radii of the smaller circles. But as it turns out, there’s a much easier way to do this.
The key is this: nothing forbids us from positioning PQ on the diameter of the big circle. That would make the diameter of the big circle 6. Furthermore, it means the smaller circles are equal in size (with diameter 3):