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

Let the radii be r₁ and r₂.
Let the angles subtend by the arcs in two circles be θ₁ and θ₂.
l = θ r where θ is the angle, l the length of an arc and r the radius of the circle.
θ₁ = 60^o = 60 × = radian
θ₂ = 75^o = 75 × = radian
r₁ = r₂
r₁ / r₂ = =
Therefore the required ratio is 5:4.