Consider a Cartesian coordinate system on a plane with origin #O#, axis #OX# (abscissa) and axis #OY# (ordinate).
A circle defined by equation #x^2+y^2=16# has a radius #R=sqrt(16)=4# and a center at origin #O#.
Point #A=(4cos theta, 4sin theta)# lies on this circle such that angle #/_XOA=theta# (counterclockwise from axis #OX# to radius #OA#)
Point #B=(4cos(theta+60^o), 4sin(theta+60^o))# also lies on this circle making an angle between X-axis and radius #OB# larger than #/_XOA# by #60^o# counterclockwise.
So, #/_XOB=/_XOA+60^o#
Therefore, the angle between radiuses #OA# and #OB# is #/_AOB=60^o#
Now it is obvious that triangle #Delta AOB# is equilateral since #OA=OB# as radiuses and #/_AOB=60^o#.
Therefore, #AB=OA=OB=4#.
