Question

If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, then the ratio of the radii of the circles is 

A. 22 : 13 

B. 11 : 13 

C. 22 : 15 

D. 21 : 13

Answer 1

Let radius of two circles be the r₁ and r₂ 

Let θ₁ and θ₂ be the subtend angles of arcs of two circles 

i.e. θ₁=65° and θ₂=110° 

We know that arc length, 

l = r × θ 

Here, arc lengths of two circles are same. 

∴ r₁×θ₁=r2×θ₂

∴ r₁ :r₂ =22:13