Draw the perpendicular from the center O to the cord AB, and let the point C represents its intersection with the chord AB.

The length |OC| is the distance of interest, d.

Notice that the point C bisects the chord AB. It is because the triangle OAB is isosceles having congruent sizes OA and OB (radii).

Now from the right-angled triangle OAC you have 

d =  =  =  =  = 15.

Thus the distance d is 15 cm.

Answer. The distance of O from AB is 15 cm.