Question 168
Draw two circles of the same center, one of radius $1~\mathrm{cm}$ and the other of radius $3~\mathrm{cm}$. In the region outside the circle of radius $1~\mathrm{cm}$ and inside the radius $3~\mathrm{cm}$, draw circles that are simultaneously tangent to the two circles, as shown in the following figure.
a) What should be the radius of these circles?
b) What is the maximum number of these circles, if they do not overlap?
a) What should be the radius of these circles?
b) What is the maximum number of these circles, if they do not overlap?