A thin string of length 220cm is divided (without cutting it up) into n parts in the ratio 1:2:3: ...n
a) Show that the length of the longest segment is 440/n+1 cm
b) The string is made to form a circle so that the ends just touch each other
(i) Find the radius of this circle
(ii) Show that the angle subtended at the center by the largest segment in part (a) is approximately 12.57/n+1
(iii) Hence find the smallest value of n for which this angle is less than π/12 radians ​