Two circles, C_{1} and C_{2}, of radius 1 are tangent to each other and to a line. A third circle C_{3} is tangent to C_{1}, C_{2}, and the line. Two chains of circles are formed as follows. The first circle in the chain is C_{3}. In one chain, the n+1^{st} circle is tangent to the n^{th} circle, C_{1}, and the line (as shown in the figure below). In the other chain, the role of C_{1} is played by C_{2}. A picture of C_{1}, C_{2}, C_{3}, and the two chains is shown below.