Angle in radians = Angle in degrees × \(\frac{\pi}{180}\)
θ = 1/r Where θ is central angle, L = length of arc, r = radius
Therefore θ1 = 75 x \(\frac{\pi}{180}\) = \(\frac{5\pi}{12}\)
θ2 = 120 x \(\frac{\pi}{180}\) = \(\frac{2\pi}{3}\)
l = r × θ
Now, as the length is the same
Therefore r1 x θ1 = r2 x θ2
Therefore the ratio of their radii is 8 : 5