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

Step-by-step explanation:

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

Now, 60∘=3π radian and 75∘=125π radian

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then

θ=rl or l=rθ

∴l=3r1π and l=12r25π

⟹3r1π=12r25π

⟹r1=4r25

⟹r2r1=45

Answer 2

Answer:

then angle substened by an arc at the centre of first circle is θ = 60° = π /3 radian Angle subtended by an arc at the centre of second circle is = 75° = 75π /180 = 5π /12 r

2From formula : Length of arc ( l ) = radius (r) x angle (θ) ∴ Length of arc of first circle = π /3 x r1 Length of arc of second circle = 5π /12 x r2