Question

6. Find the ratio of the radii of the circles in which
the arcs of the same length subtend the angles
60° and 45° respectively at their centres.
​

Answer 1

Step-by-step explanation:

As we have given the arcs of the same length subtend the angles

60° and 45°

we know ,

S(arc length) =r (radius ) x Φ(angle subtended at the centre of the circle)

s = r . Φ

r = s /Φ

let us consider, the radii of the circles are r1 and r2 , angles subtended are Φ1 and Φ2 And arcs are s1 and s2

therefor

r1 = s1 / Φ1

r2 = s2 / Φ2

Φ1 = 60°

Φ2 = 45°

therefor the ratios of their radius are

( r1 ) /( r2 ) = (s1 / Φ1)/(s2 / Φ2)

As we have given,

s1 = s2

therefor,

(r1) / (r2) = ( s1 / Φ1) / (s1 /Φ2)

= (Φ2 / Φ1)

= 45° / 60°

= 3 / 4

therefor the ratio of their radii is

r1 : r2 = 3:4