Plz asap tangents of a circles problems

The radius of circle is 5.

AO = AB + OB

AB = 8
OB = Radius of circle = 5

So, 

AO = 8 +5 = 13

The tangent of the circle is at 90 degrees to its radius. So we can say that triangle ACO is a right angled triangle, with side AO the hypotenuse.

Using the Pythagorean theorem we can find the length of tangent AC.

13² = AC² + 5²
AC² =  169 - 25 = 144
AC = 12

So, the length of side AC is 12

What are the choices