CircleHardBloom L3
Question
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 $60^{\circ}$. The area enclosed by these tangents and the arc of the circle is:
Options
A.$\frac{2}{\sqrt{3}} - \frac{\pi}{6}$
B.$\sqrt{3} - \frac{\pi}{3}$
C.$\frac{\pi}{3} - \frac{\sqrt{3}}{6}$
D.$\sqrt{3}\left( 1 - \frac{\pi}{6} \right)$
Solution
[Key Concept: Pair of tangents to the unit circle: the angle between them gives the chord-of-contact triangle area.]
$r = 1;L = \sqrt{3}$
area of quadrilateral $= \sqrt{3}$
area of sector $= \frac{1}{2} \cdot 1 \cdot \frac{2\pi}{3} = \frac{\pi}{3}$
shaded region $= \sqrt{3} - \frac{\pi}{2}$
Create a free account to view solution
View Solution FreeMore Circle Questions
Let $x,y$ be real variable satisfying the $x^{2} + y^{2} + 8x - 10y - 40 = 0$. Let $a = \max\left( \sqrt{(x + 2)^{2} + (...y = √3 x + c1 & y = √3 x + c2 are two parallel tangents of a circle of radius 2 units, then c1 - c2| is equa...The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq units. Then the equation of the ci...The length of the common chord of the circle x2 + y2 + 4x + 6y + 4 = 0 and x2 + y2 + 6x + 4y + 4 = 0 is-...The intercept on the line y = x by the circle x2 + y2 - 2x = 0 is AB. Equation of the circle on AB as a diameter is...