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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