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If the arcs of the same length in two circles subtend angles 75° and 120° at the centre, find the ratio of their radii

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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

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