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Two arcs of the same length substend |
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Answer» here is your answer If in two circles, arcs of the same length subtend angles 60 ∘ and 75 ∘ at the CENTRE, find the ratio of their radii. Let the radii of the two circles be r 1
and r 2
. Let an arc of length I subtend an angle of 60 ∘ at the centre of the circle of radius r 1
, while let an arc of length I subtend an angle of 75 ∘ at the centre of the circle of radius r 2
. Now, 60 ∘ = 3 π
radian and 75 ∘ = 12 5π
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= r l
or l=rθ ∴l= 3 r 1
π
and l= 12 r 2
5π
⟹ 3 r 1
π
= 12 r 2
5π
⟹r 1
= 4 r 2
5
⟹ r 2
r 1
= 4 5 |
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