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