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Q.

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


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a

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b

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c

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d

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answer is C.

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Detailed Solution

We know that the arc length is l=rθ  .
Converting the given angle into radian, and we have
For 60 ∘  ,
θ=60× π 180 = π 3  
For 75 ∘  ,
θ=75× π 180 = 5π 12  
Given that their lengths are equal. Then,
l 1 = l 2 r 1 θ 1 = r 2 θ 2 r 1 r 2 = θ 2 θ 1 = 5 12 π 3 = 5 12 × 3 1 = 5 4  
Hence, the correct option is 3.
 
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