Geometry

so if a 83 degree sector of a circle has an area of 60 pi, then we can find some ratios. 83/360 = 60pi/ (area of cricle) so the area of the cirlc ewould be 21600/83 pi so the radius of the circle would be 60sqrt6 / sqrt83 or \(\frac{60\sqrt{498}}{83}\). 

Area =  pi r^2 * (83/360)

60 pi = pi* r^2 * (83/360)

r^2  = (60 * 360) / 83

r = sqrt [ 60 * 360 / 83 ]  ≈ 16.13