A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of $60^o$. The area enclosed by these tangents and the arc of the circle is
A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of $60^o$. The area enclosed by these tangents and the arc of the circle is
- A
$\frac{2}{{\sqrt 3 }} - \frac{\pi }{6}$
- B
$\sqrt 3 - \frac{\pi }{3}$
- C
$\frac{\pi }{3}-\frac{{\sqrt 3 }}{6}$
- D
$\sqrt 3 \,\left( {1\; - \;\frac{\pi }{6}} \right)$
Similar Questions
If the tangents at the points $P$ and $Q$ on the circle $x ^2+ y ^2-2 x + y =5$ meet at the point $R \left(\frac{9}{4}, 2\right)$, then the area of the triangle $PQR$ is
If the tangents at the points $P$ and $Q$ on the circle $x ^2+ y ^2-2 x + y =5$ meet at the point $R \left(\frac{9}{4}, 2\right)$, then the area of the triangle $PQR$ is
- [JEE MAIN 2023]
A line $lx + my + n = 0$ meets the circle ${x^2} + {y^2} = {a^2}$ at the points $P$ and $Q$. The tangents drawn at the points $P$ and $Q$ meet at $R$, then the coordinates of $R$ is
A line $lx + my + n = 0$ meets the circle ${x^2} + {y^2} = {a^2}$ at the points $P$ and $Q$. The tangents drawn at the points $P$ and $Q$ meet at $R$, then the coordinates of $R$ is
$S_1$ 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
$S_1$ 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
$x = 7$ touches the circle ${x^2} + {y^2} - 4x - 6y - 12 = 0$, then the coordinates of the point of contact are
$x = 7$ touches the circle ${x^2} + {y^2} - 4x - 6y - 12 = 0$, then the coordinates of the point of contact are
The line $lx + my + n = 0$ is normal to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$, if
The line $lx + my + n = 0$ is normal to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$, if