Problem 79E

79. The figure shows two circles $C$ and $D$ of radius 1 that touch at $P$. The line $T$ is a common tangent line; $C_{1}$ is the circle that touches $C, D$, and $T ; C_{2}$ is the circle that touches $C, D$, and $C_{1}$; $C_{3}$ is the circle that touches $C, D$, and $C_{2} .$ This procedure can be continued indefinitely and produces an infinite sequence of circles $\left\{C_{n}\right\}$. Find an expression for the diameter of $C_{n}$ and thus provide another geometric demonstration of Example 8.

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