If two circular arcs of the same length subtend angles of 60° and 80° at their respective centres, then the ratio of their radii is

Question

If two circular arcs of the same length subtend angles of 60° and 80° at their respective centres, then the ratio of their radii is (A) (3/4) (B) (4/3) (C) (√3/2) (D) (9/16)

Tardigrade Admin · Accepted Answer

Given that, S 1= S 2 If the radii are r1 and r2, then beginarrayl r1 × θ1=r2 × θ2 ⇒ r1((60 π/180))=r2((80 π/180)) ldots .[∵ s = r θ] ⇒ (r1/r2)=(80/60)=(4/3) endarray

Q. If two circular arcs of the same length subtend angles of $6 0^{\circ}$ and $8 0^{\circ}$ at their respective centres, then the ratio of their radii is

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{3}{2}$

$\frac{9}{16}$

Given that, $S_{1} = S_{2}$
If the radii are $r_{1}$ and $r_{2}$ , then
$r_{1} \times θ_{1} = r_{2} \times θ_{2} \Rightarrow r_{1} (\frac{60 π}{180}) = r_{2} (\frac{80 π}{180}) \dots . [∵ s = r θ] \Rightarrow \frac{r _{1}}{r _{2}} = \frac{80}{60} = \frac{4}{3}$

Q. If two circular arcs of the same length subtend angles of 60∘ and 80∘ at their respective centres, then the ratio of their radii is

43​

34​

23​​

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