Ab is tangent to circle o. find the length of the radius.

This is the concept of geometry;
given that the tangent of circle is always perpendicular to the radius, to solve for the measure of the radius will be given by the pythagorean theorem.
c^2=a^2+b^2
where;

a=base=radius
b=height=hypotenuse
c=hypotenuse

substituting the values in our formula we get:
11.7^2=8^2+r^2
r^2=11.7^2-8^2
r^2=136.89-64
r^2=72.89
squaring both sides to get the value of r we get:
r=sqrt (72.89)
r=8.5376 in