smc

Question

On a sheet of paper, Isabella draws a circle of radius 2, a circle of radius 3, and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly k 0 lines. How many different values of k are possible?

Accepted Answer

Isabella can get 0 lines if the circles are concentric, 1 if internally tangent, 2 if overlapping, 3 if externally tangent, and 4 if non-overlapping and not externally tangent. There are 5 values of k.