How the tangent to a circle is a special case of the secant?

In the adjoining figure, a circle touches all the four sides of a quadrilateral $\mathrm{ABCD}$ whose sides are $\mathrm{AB}=6\mathrm{cm}, \mathrm{BC}=9\mathrm{cm}$ and $\mathrm{CD}=8 \mathrm{cm}$. Find the length of side $\mathrm{AD}$.
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In the given figure, the tangent at a point $\mathrm{C}$ of a circle and diameter $\mathrm{AB}$ when extended intersect at $\mathrm{P}. \mathrm{I}\mathrm{f} \angle \mathrm{P}\mathrm{C}\mathrm{A}=110°$, find $\angle \mathrm{C}\mathrm{B}\mathrm{A}$.

A quadrilateral $\mathrm{}\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\mathrm{}$ is drawn to circumscribe a circle (see Fig.). Prove that
$\mathrm{A}\mathrm{B}+\mathrm{C}\mathrm{D}=\mathrm{A}\mathrm{D}+\mathrm{B}\mathrm{C}$
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In the figure below, $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle drawn from an external point $\mathrm{P}$. $\mathrm{CD}$ is a third tangent touching the circle at $\mathrm{Q}$. If $\mathrm{P}\mathrm{B}=10 \mathrm{c}\mathrm{m}$ and $\mathrm{C}\mathrm{Q}=2 \mathrm{c}\mathrm{m},$ what is the length $\mathrm{PC}$ ?