Let the radii of the two circles be r1 and r2 . Let an arc of length l1 subtends an angle of 60° at the centre of the circle of radius r1 , whereas let an arc of length l2
subtends an angle of 75° at the centre of the circle of radius r2.
Now, we have,
\( 60°=\dfrac{\pi}{3}radian\)
\( 75°=\dfrac{5\pi}{12}radian\)
We know that,
in a circle of radius r unit, if an angle θ radian at the centre is subtended by an arc of length l unit then
\( θ=\dfrac{1}{r}\)
l=rθ
Hence we obtain,
\(1= \dfrac{r_1\pi}{3}\) and
\(1= \dfrac{r_25\pi}{12}\)
according to the question
11 =12
thus we have,
\( \dfrac{r_1\pi}{3\pi}=\dfrac{r_25\pi}{12}\)
\( r_1=\dfrac{r_25}{4}\)
\( \dfrac{r_1}{r_2}=\dfrac{5}{4}\)
Hence , the ratio of the radii is 5:4
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