S_1 and S_2 are two concentric circles of rad | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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

Similar Questions

The equation of the circle whose radius is $5$ and which touches the circle ${x^2} + {y^2} - 2x - 4y - 20 = 0$ externally at the point $(5, 5)$ is

Let $\alpha$ be an integer multiple of $8$. If $S$ is the set of all possible values of $\alpha$ such that the line $6 x + 8 y + \alpha = 0$ intersects the circle $x^2 + y^2 - 4 x - 6 y + 9 = 0$ at two distinct points,then the number of elements in $S$ is

In a $\triangle ABC$,a point $D$ is chosen on $BC$ such that $BD:DC = 2:5$. Let $P$ be a point on the circumcircle of $\triangle ABC$ such that $\angle PDB = \angle BAC$. Then $PD:PC$ is:

The length of the intercept on the line $4x - 3y - 10 = 0$ by the circle $x^2 + y^2 - 2x + 4y - 20 = 0$ is

$A$ rectangle is inscribed in a circle with a diameter lying along the line $3y = x + 7$. If the two adjacent vertices of the rectangle are $(-8, 5)$ and $(6, 5)$,then the area of the rectangle (in $sq. units$) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module