Question

Don’t be slow pls. just do what the question says.

Answer 1

r = 3.8

Step-by-step explanation

If AB is tangent to the circle at A, and AO is the radius of the circle, then angle OAB is a right angle. Therefore we have a right triangle:

The hypotenuse of the triangle is segment BO, which by the segment addition postulate is:

`\begin{gathered} BO=BC+CO \\ BO=6+r \end{gathered}`

Then we have one leg of the triangle which is AB = 9 and the other leg is r.

Using he pythagorean theorem we can find r:

`\begin{gathered} BO^2=AO^2+AB^2 \\ (r+6)^2=r^2+9^2 \end{gathered}`

Expanding the binomial on the left side:

`r^2+12r+36=r^2+81`

Note that we have r² on both sides, so if we subtract r² from both sides:

`\begin{gathered} r^2-r^2+12r+36=r^2-r^2+81 \\ 12r+36=81 \end{gathered}`

We have a linear equation. Solving for r:

`\begin{gathered} 12r=81-36 \\ 12r=45 \\ r=(45)/(12) \\ r=(15)/(4) \\ r=3.75\approx3.8 \end{gathered}`