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Question

A pair of tangents is drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of 60. The area enclosed by these tangents and the arc of the circle is

A
23π6 sq. units
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B
3π3 sq. units
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C
π336 sq. units
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D
3(1π6) sq. units
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Solution

The correct option is B 3π3 sq. units
r=1
Let length of tangent be L
Now the quadrilateral formed by the tangents and radii is cyclic quadrilateral
A+O=180°
tan60=Lr
L=3

Area of shaded region =Lr12r2θ=3π3 sq. units

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