Question

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

Answer 1

Answer:

The Ratio is 5:4

Step-by-step explanation:

Let the radius of the 2 circles be R1 and R2.  Let the length of the arc be L.

We know that,

360°= 2π

60°=π/3 radian   75°=5π/12 radian

We know that,

theta = L/r

or L=r*theta

L= R1π/3 .............................(1)

L= R2*5π/12 ............................(2)

Equating equation (1) and (2), we get,

R1π/3 = R2*5π/3

On cancelling 3 and 12, and π on both sides we get,

R1 = R2*5/4

R1/R2 = 5/4

R1:R2 = 5:4

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