# Tangents Secants and Circles...Oh My

Geometry Level 1

In the above diagram, line segment $$\overline{PT}$$ is tangent to both circle $$O$$ and circle $$O'.$$ Given the following three lengths: $\lvert\overline{AB}\rvert = 35, \lvert\overline{PC}\rvert = 30, \lvert\overline{CD}\rvert = 20,$ what is $$\lvert\overline{PA}\rvert?$$

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