Question

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

Answer 1

Let the radii of the two circles be r1 and r2. Let an arc of length l subtend an angle of 60° at the centre of the circle of radius r1, while let an arc of length l subtend an angle of 75° at the centre of the circle of radius r2. 

Now, 60°=π/3 radian and 75° = 5π/12 radian

We know that in a circle of radius r an angle unit, if an arc of length l unit subtends θ

Thus, the ratio of the radii is 5:4.