Question

ab is tangent to circle o at b. find the length of the radius r fur ab=5 and ao=8.6

Answer 1

Look at the picture.

We must use the Pythagorean theorem:

$AB^2+OB^2=AO^2\\\\5^2+r^2=8.6^2\\\\25+r^2=73.96\qquad\text{subtract 25 from both sides]\\\\r^2=48.96\to r=\sqrt{48.96}\\\\\boxed{r\approx7}$

Answer: The radius is equal 7.