20.116 Let $C_{1}$ and $C_{2}$ be two circles of radius 1 that are tangent to each other in the same plane. The number of circles of radius 3 that are tangent to both $C_{1}$ and $C_{2}$ in this plane is
(A) 2.
(B) 4.
(C) 5.
(D) 6.
(E) 8.
(44th American High School Mathematics Examination, 1993)
[Solution] As shown in the figure, there are 6 cases, meaning there are 6 circles with a radius of 3 that are tangent to both $C_{1}$ and $C_{2}$:
Therefore, the answer is $(D)$.