Question

In the picture, point C is a point of tangency.815mDA=DE =

Answer 1

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:

$\begin{gathered} \text{hypothenus}^2=opposite^2+adjacent^2 \\ \end{gathered}$$\begin{gathered} DA^2=DC^2_{}+CA^2 \\ \end{gathered}$$\begin{gathered} DA^2=15^2+8^2=225+64=289 \\ DA=\sqrt[]{289}=17 \end{gathered}$

Thus:

$DA=17$

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:

$DE=DA-AE$$DE=17-8=9$

Therefore:

$DE=9$