Let the radii of the two circles be r_{1} and r_{2} . Let an arc of length l_{1} subtends an angle of 60° at the centre of the circle of radius r_{1} , whereas let an arc of length l_{2}

subtends an angle of 75° at the centre of the circle of radius r_{2}.

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

1_{1} =1_{2}

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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