Question

If AB=7 and AO=17.4, what is the length of the radius (r)? Round to the nearest tenth. (Will mark brainliest)

Answer 1

We know that B is a point of tangency, so as known from the problem $\overline{AB}$ is tagent to the circle in this point. We also know that the segment line $\overline{BO}$ is perpendicular (given that this segment is the radius) to the previous tangent, therefore we are in the presence of a right triangle. Then, the following equation is true:

$\overline{AB}^{2}+\overline{BO}^{2}=\overline{AO}^{2}$

being $\overline{BO}=r$

Then:

$r^{2}=\overline{AO}^{2}-\overline{AB}^{2}$
$r=\sqrt{\overline{AO}^{2}-\overline{AB}^{2}}$
$r=\sqrt{17.4^{2}-7^{2}}$
$r=15.9$ 

Answer 2

The radius equals 5.5