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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Solution

The radius of any circle is defined as

Radius= Length of arc Angle subtended

Consider that the length of the arc maintained constant, then

Radius∝ 1 Angle subtended

The ratio of radii when the angle subtended are 60° and 75° respectively.

r 60 r 75 = 75° 60° = 5 4

Thus, the radii are in the ratio 5:4 .

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If, in two circles, arcs of the same length subtend angles $60^{0}$ and $75^{0}$ at the centre, find the ratio of their radii.

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