[tex] \Large \mathbb{SOLUTION:} [/tex]
[tex] \begin{array}{l} \bold{Given:} \: \begin{cases}\: AB = \sf 10 \\ \: BC = \sf 5 \\ \: CD = \sf 13 \end{cases} \\ \\ \bold{Required:}\: AD \\ \\ \textsf{Let the segment from side }AB\textsf{ be x. Note that} \\ \textsf{all tangents which meet at the same point are} \\ \textsf{equal in length.} \\ \\ \textsf{Refer to the attached picture.} \\ \\ \textsf{Now we can solve for }AD. \\ \\ AD = \sf 10 - x + x + 8 \\ \\ \boxed{AD = \sf 18} \end{array} [/tex]
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