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

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


  1. A
  2. B
  3. C
  4. D

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    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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