An elastic belt is placed round the rim of a pulley of radius 5 cm. One point on the belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from O.find the length of the belt that is in contact with the rim of the pulley.

Dear Student,
Refer the following figure:

Now in Triangle OAP
the angle at centre can be calculated by trigonometry  sin $\theta$= 5/10= 1/2    -------->   θ= 60^o   
total angle made by AB = 2 $\theta$ = 120^o

so length of belt in contact = (360-120) 2$\mathrm{\pi }$(5)/360     =   20*3.14/3=  20.933 cm