S_1 and S_2 are two concentric circles of rad | vedclass

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(B) Let $O$ be the center of the concentric circles. Let the two parallel tangents to $S_1$ touch $S_1$ at points $M$ and $N$. Since the tangents are

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$\frac{2\pi}{3}$

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(B) Let $O$ be the center of the concentric circles. Let the two parallel tangents to $S_1$ touch $S_1$ at points $M$ and $N$. Since the tangents are parallel,$MN$ is a diameter of $S_1$,so $OM = ON = 1$.Let the tangents intersect $S_2$ at points $A$ and $B$. In $	riangle OMA$,$OM = 1$ and $OA = 2$ (radius of $S_2$).Since $AM$ is a tangent to $S_1$,$\angle OMA = 90^\circ$. Thus,$\cos(\angle MOA) = \frac{OM}{OA} = \frac{1}{2}$.Therefore,$\angle MOA = \frac{\pi}{3}$.Similarly,for the other tangent,$\angle NOB = \frac{\pi}{3}$.The angle subtended by the arc $AB$ at the center is $\angle AOB = \pi - (\angle MOA + \angle NOB) = \pi - (\frac{\pi}{3} + \frac{\pi}{3}) = \frac{\pi}{3}$.The length of the arc $AB = r \cdot 	heta = 2 \cdot \frac{\pi}{3} = \frac{2\pi}{3}$.

$S_1$ and $S_2$ are two concentric circles of radii $1$ and $2$ respectively. Two parallel tangents to $S_1$ cut off an arc from $S_2$. The length of the arc is

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