Two arcs of same length of two different circles subtended angles of 25° and 75° at their centres respectively . Then the ratio of the radii of the circles is

Question

Two arcs of same length of two different circles subtended angles of 25° and 75° at their centres respectively . Then the ratio of the radii of the circles is (A) 3: 1 (B) 1: 3 (C) 1: 2 (D) 2: 1

Tardigrade Admin · Accepted Answer

Length of arc , l = r θ ∴ (r1/r2)=(l/θ1 /l / θ2) =(θ2/θ1) =(75/25) =(3/1)

Q. Two arcs of same length of two different circles subtended angles of 25° and 75° at their centres respectively . Then the ratio of the radii of the circles is

3 : 1

1 : 3

1 : 2

2 : 1

Length of arc , $l = r θ$
$∴ \frac{r _{1}}{r _{2}} = \frac{l / θ _{1}}{l / θ _{2}} = \frac{θ _{2}}{θ _{1}}$
$= \frac{75}{25}$
$= \frac{3}{1}$

Q. Two arcs of same length of two different circles subtended angles of 25° and 75° at their centres respectively . Then the ratio of the radii of the circles is

3 : 1

1 : 3

1 : 2

2 : 1

Length of arc , l=rθ ∴r2​r1​​=l/θ2​l/θ1​​=θ1​θ2​​ =2575​ =13​

Length of arc , $l = r θ$
$∴ \frac{r _{1}}{r _{2}} = \frac{l / θ _{1}}{l / θ _{2}} = \frac{θ _{2}}{θ _{1}}$
$= \frac{75}{25}$
$= \frac{3}{1}$