If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Given: Two circles with arcs of the same length and subtend angles 60° and 75° at the centre respectively.

Let L be the length of the arcs..

Let r₁ be the radius of the first circle and let r₂ be the radius of the second circle.

We know the θ = ⇒ r =

∴ r₁: r₂ = : = θ₂:θ₁

⇒ r₁: r₂ = 75 × : 60 × (∵ θ is measured in radians and 1° = radian)

⇒ r₁: r₂ = 75: 60 = 5:4

∴ r₁: r₂ = 5:4