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प्रश्न
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii
उत्तर
Let r1 and r2 be the radii of the two circles and l be the length of the arc.
Given central angle θ1 = 60°
θ1 = `60 xx pi/180 = pi/3` radians
θ2 = 75°
θ2 = `75 xx pi/180 = (5pi)/12` radians
Given that l = r1θ1 = r2θ2
`"r"_1 pi/3 = "r"_2 (5pi)/12`
`"r"_1/"r"_2 = (5pi)/12 xx 3/pi`
`"r"_1/"r"_2 = 5/4`
r1 : r2 = 5 : 4
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