Geometry
# Tangent and Secant Lines

Circle \(O\) with radius \(2\) is inscribed in a trapezoid \(ABCD\) such that \(\overline{AD} \parallel \overline{BC}\) and \(\lvert \overline{CD} \rvert = 8.\) If \(\angle{A} = \angle{B} = 90^{\circ},\) what is the area of \(ABCD?\)

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

In the above diagram, \(\overline{BC}, \overline{AE}\) and \(\overline{AF}\) are tangent to circle \(O\) at \(D, E\) and \(F,\) respectively. If \[\lvert \overline{AC} \rvert = 25, \lvert \overline{AB} \rvert = 20, \lvert \overline{BC} \rvert = 15,\] what is the area of quadrilateral \(CDOF?\)

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

Given the quadrilateral and inscribed circle, what is the missing side length?

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