Question

B is a poiny of tangency. if ab=8 and ad=5, find dc.

Answer 1

3.9

Explanation:

We can see that a right triangle ABC is formed. Therefore, we can calculate the value of DC (which would be the radius of the angle) by means of the Pythagorean theorem.

We can establish the following equation, let r be the value of DC and BC, hence:

`\begin{gathered} AC^2=AB^2+BC^2 \\ (AD+DC)^2=AB^2+DC^2 \\ \text{ Replacing:} \\ (5+r)^2=8^2+r^2 \\ 25+10r+r^2=64+r^2 \\ 10r=64-25 \\ r=(39)/(10)=3.9 \\ \text{ Therefore:} \\ DC=r=3.9 \end{gathered}`

Therefore, the value of DC is equal to 3.9