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If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

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Let the radii of the two circles be and. Let an arc of length l subtend an angle of 60° at the centre of the circle of radius r1, while let an arc of length l subtend an angle of 75° at the centre of the circle of radius r2. Now, 60° =and 75° = We know that in a circle of radius r unit,...
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Let the radii of the two circles be and. Let an arc of length l subtend an angle of 60° at the centre of the circle of radius r1, while let an arc of length l subtend an angle of 75° at the centre of the circle of radius r2.

Now, 60° =and 75° =

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.

Thus, the ratio of the radii is 5:4.

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