Question

Can someone answer this with explanations please

Answer 1

In the figure assume that the circle are mutually tangent and that the circle with centre at A has radius 1. The lines AB and AC are tangent to the circle with centre O at B and C respectively. If the area of the shaded region is π/4, the radius of the circle centered

Let, ∠CAB=θ

Then, area of sector,

360

θ

π(1)

2

=

4

π

θ=90

∘

Now, the line joining the centre of the circle bisects the angle formed between two tangets, hence, ∠CAO=45

∘

Now, In △AOC

∠ACO=90

∘

(Angle between the tangent and the radius)

sin45=

AO

OC

2

1

=

r+1

r

r+1=r

2

r=

2

−1

1

(Rationalizing)

r=

2

+1

Step-by-step explanation:

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