Q. 55.0( 1 Vote )
If, in two circles, arcs of the same length subtend angles of 60o and 75o at the centre, find the ratio of their radii.
Let the radii be r1 and r2.
Let the angles subtend by the arcs in two circles be θ1 and θ2.
l = θ r where θ is the angle, l the length of an arc and r the radius of the circle.
θ1 = 60o = 60 × = radian
θ2 = 75o = 75 × = radian
r1 = r2
r1 / r2 = =
Therefore the required ratio is 5:4.
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