UPSC 2015 CDS I Math Paper

Radius of each smaller circle =

d

2

Now, AB = BC = CA = d
Therefore, ΔABC is an equilateral triangle.
Let O be the centre and R be the radius of the bigger circle.
∠OBD = 30°
In right ΔOBD,
cos‌30°=

( d 2 )

OB

⇒

√3

2

=

d

2OB

⇒OB=

d

√3

Radius of the bigger circle,R=(

d

√3

+

d

2

)
Therefore, area of the bigger circle=πR2
=‌‌

πd2(√3+2)2

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