A physics experiment is set up using two pulleys, a string, and a weight as shown below. The larger pulley has a radius of 14 centimeters, and the smaller pulley has a radius of 8 centimeters. The distance between the centers of the pulleys is 56 centimeters. The string is pulled tightly across both pulleys so that AB is a common tangent of the pulleys. Find the length of string from A to B to the nearest tenth of a centimeter.

A physics experiment is set up using two pulleys, a string, and a weight as shown below. The larger pulley has a radius of 14 centimeters, and the smaller pulley has a radius of 8 centimeters. The distance between the centers of the pulleys is 56 centimeters. The string is pulled tightly across both pulleys so that AB is a common tangent of the pulleys. Find the length of string from A to B to the nearest tenth of a centimeter.