2.0k views
1 vote
In the picture, point C is a point of tangency.815mDA=DE =

In the picture, point C is a point of tangency.815mDA=DE =-example-1
User Camcam
by
8.4k points

1 Answer

1 vote

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

User Anton Krouglov
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories