Two circles having same are length subtend angle $60^{o}$ and $30^{o}$ at their centers, then their ratio of their radii are

2 : 1

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1 : 2

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1 : 1

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n o n e

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Solution

The correct option is B $1 : 2$
As angle at center = $\frac{a r c l e n g t h}{r a d i u s o f c i r c l e}$
$\Rightarrow \frac{60}{180} \times π = \frac{l}{r_{1}} - - (1) a n d 30 \times \frac{π}{180} = \frac{l}{r_{2}} - - - (2)$
$E q^{2} (1) \div E q^{2} (2) = \frac{60}{30} = \frac{r_{2}}{r_{1}} \Rightarrow \frac{r_{2}}{r_{1}} = 2$
$\Rightarrow r_{1} / r_{2} = 1 / 2 = 1 : 2 \Rightarrow (B)$

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Two circles having same are length subtend angle 60o and 30o at their centers, then their ratio of their radii are

The correct option is B 1:2As angle at center = arclengthradiusofcircle⇒60180×π=lr1−−(1)and30×π180=lr2−−−(2)Eq2(1)÷Eq2(2)=6030=r2r1⇒r2r1=2⇒r1/r2=1/2=1:2⇒(B)

Two circles having same are length subtend angle $60^{o}$ and $30^{o}$ at their centers, then their ratio of their radii are