Answer:
6.24 units
Explanation:
Recall that the angle between a tangent AB and the radius, BO is always 90 degrees.
Therefore, triangle ABO is a right triangle.
Applying the Pythagorean Theorem:
[tex]\begin{gathered} AO^2=AB^2+BO^2 \\ \implies8^2=5^2+r^2 \end{gathered}[/tex]We solve the equation above for r:
[tex]\begin{gathered} r^2=8^2-5^2 \\ r^2=64-25 \\ r^2=39 \\ r=\sqrt[]{39} \\ r\approx6.24 \end{gathered}[/tex]The length of the radius is approximately 6.24 units.