A tangent to a circle is a line intersecting the circle at exactly one point. Can you prove that the line from the center of the circle to the point of tangency is perpendicular to the tangent line?

**Note:** The above diagram is not drawn to scale.

**Note:** The above diagram is not drawn to scale.

**Note:** The above diagram is not drawn to scale.

In the above figure, \(A, B\) and \(T\) are three points lying on a circle. If \(\overline{PT}\) is a tangent line of the circle and \[\lvert\overline{AB}\rvert=7 \text{ and }\lvert\overline{PT}\rvert=12,\] where \(\lvert\overline{AB}\rvert\) denotes the length of \(\overline{AB},\) what is \(\lvert\overline{PA}\rvert ?\)

**Note:** The above diagram is not drawn to scale.

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