Answer:
[tex]AB=12\sqrt{3}\ cm[/tex]
Step-by-step explanation:
If AB is tangent to the circle, then angle ABO is right angle and triangle AOB is special [tex]30^{\circ}-60^{\circ}-90^{\circ}[/tex] triangle. In this triangle, the leg that is opposite to the angle of 30° is half of the hypotenuse. Thus,
[tex]AO=2BO=2\cdot 12=24\ cm.[/tex]
By the Pythagorean theorem,
[tex]AB^2=AO^2-BO^2,\\ \\AB^2=24^2-12^2,\\ \\AB^2=576-144=432,\\ \\AB=12\sqrt{3}\ cm.[/tex]
