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Question

If the arcs of the same length in two circles substend angles 65 and 110 at the centre, find the ratio of their radii.


Solution

Let, C1 and C2 are two circles with same Arc length l.

That is AB = CD = l

Let, θ1 and θ2 are two angles subtended by arc AB and CD on respective circles.

Let, OA = OB = r         [radius of C1]

and OC = OA = R       [radius of C2]

Also,

θ1=65=(65π180)cand   θ2=110=(110π180)c

We know

θ=arcradius   For C1   θ1=ABr
   θ1=lr         . . . (i)

    r=1θ1

For    C2

θ2=CDR   θ2=lR
   R=lθ2        . . .(ii)

From (i) and (ii)

rR=lθ1lθ2=θ2θ1=110π18065π180=2213

r : R = 22 : 13


Mathematics
RD Sharma
Standard XI

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