A lot of people seemed stumped with this one, so I thought I would provide a full solution. At first sight it seem there is not enough information given. You are given the length of the middle line (which in the general proof below I will call M) and the distance between the circle centres (which I will call C), but not the radius (r) of the two circles. This proof below demonstrates that the length of the base is not dependent upon r, but only on M and C.
So the formula for the base is C(2M-C)/(M-C). Plug in the values given for M and C (60 and 24 respectively) and the length of the base turns out to be 64.