the picture in the attached figure
we know that
if AB is tangent to circle O at B
then
OB is the radius and is perpendicular to AB
therefore
in the right triangle ABO
applying the Pythagoras Theorem
AO²=AB²+OB²-------> solve for OB
OB²=AO²-AB²------> 11.7²-6²------> OB²=100.89
OB=√100.89--------> OB=10.04----------> OB=10.0 units
the answer is the option
C. 10.0
