Question

If the area of the same lengthy in 2 circles subtend angles 60 degree and 75 degree at the centre find the ratio of thier 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