Question

Q. Four small circles of radius 1 are tangent to each other and to a large circle containing them, as shown in the figure. What is the
area of the region inside the larger circle, but outside all the smaller circles?

Answer 1

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♦♦ Precise Figure : Refer to Attachment 

→ Join all the points of the smaller circle, you get a Square

→ ∠AOB = 90°, and since, all little circles are Identical, OA = OB

=> We get an isosceles Right Δ with AB = 2( 1 unit ) = 2 units
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→ Applying Pythagoras on ΔOAB, we get : OA = OB = √2 units

→ line m  is Tangent to Bigger Circle and Small Circle as well

=> OM = OA + AM = [ √2 + 1 ]units

=> Shaded Region = ar[ Bigger Circle ] - 4ar[ Smaller Circle ]
                               = π[ 2√2 - 1 ] sq. units
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