Problem #100

Two circles, C1 and C2, of radius 1 are tangent to each other and to a line. A third circle C3 is tangent to C1, C2, and the line. Two chains of circles are formed as follows. The first circle in the chain is C3. In one chain, the n+1st circle is tangent to the nth circle, C1, and the line (as shown in the figure below). In the other chain, the role of C1 is played by C2. A picture of C1, C2, C3, and the two chains is shown below.

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