Since the angle at which a tangent of a circle meets a radius of the circle is 90 degrees, the triangle ACD is a right triangle and we can apply the Pythagorean theorem to find the length of side DA, which is the hypothenus, as follows:
[tex]\begin{gathered} \text{hypothenus}^2=opposite^2+adjacent^2 \\ \end{gathered}[/tex][tex]\begin{gathered} DA^2=DC^2_{}+CA^2 \\ \end{gathered}[/tex][tex]\begin{gathered} DA^2=15^2+8^2=225+64=289 \\ DA=\sqrt[]{289}=17 \end{gathered}[/tex]
Thus:
[tex]DA=17[/tex]
Now, to find the value of DE, we observe that AE is the radius of the circle which we have been given to be 8.
Thus, we have that:
[tex]DE=DA-AE[/tex][tex]DE=17-8=9[/tex]
Therefore:
[tex]DE=9[/tex]
