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