A pair of tangents are drawn to a unit circle with centre at origin and these tangents intersect at

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10-1.Circle and System of Circles

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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

$\sqrt 3 \,\left( {1\; - \;\frac{\pi }{6}} \right)$

Solution

$r = 1$ ;$ L =\sqrt{3}$

quad $=\sqrt{3}$

sector $=\frac{1}{2} · 1 · \frac{{2\pi }}{3}$$ =\frac{\pi }{3}$

shaded region $=\sqrt{3} -$ $\frac{\pi }{3}$ Ans.

Standard 11

Mathematics

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