4 kissing circles

Question

There is a large circle with a radius of 3. Inside the circle there are three other circles; one with a radius of 2, another with a radius of 1, and the other an unknown radius labeled f. Find f. Show all work.

 

Answer 1

There must be more to this than what you have written.  For a circle to fit inside another circle, its radius must be less than the larger circle, therefore:

 

f < 3