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?

What is the area of the shaded quadrilateral shown above?

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

**Note:** the above diagram is not drawn to the scale

Note: \(\lvert\overline {AB}\rvert\) denotes the length of \(\overline {AB}.\)

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