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Question

Two tangents to the circle x2+y2=4 at the points Aand B meet at P(-4,0).

The area of the quadrilateral PAOB where O is the origin, is


A

4 sq. units

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B

62 sq. units

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C

43 sq. units

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D

None of these

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Solution

The correct option is C

43 sq. units


The explanation for the correct answer.

Step 1. Find the radius of the circle

We know that the equation of the circle x2+y2=r2, r is the radius of the circle.

The equation of a circle is x2+y2=4

So the radius of the circle is 2

Step 2. Find the length of AD

PAO is a right-angle triangle right angle at A

OP=4unit,OA=2unit

Let POA=θ

cosθ=24

=12

θ=π3

POA=POD=θ

ADO is a right aright-angle right angle at D

sinπ3=ADAOAD=32·2AD=3

Step 3. Find the area of the quadrilateral

Area of Quadrilateral PAOB=2(Area of PAO)

Area of PAO=12×OP×AD

=12×4×3=23

So the area of the quadrilateral is 2×23=43 sq. units

Hence, option(C) is the correct answer.


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