Bunuel wrote:

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. \(10(\sqrt{2} - 1)\)

B. \(20(\sqrt{2} - 1)\)

C. \(\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}\)

D. \(40(\sqrt{2} - 1)\)

E. \(\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}\)

Source: ExpersGlobal

Attachment:

Screenshot %2887%29.png

IMO C AS the diameter of large circle is 40 as the side of square is also 40

then diagonal of square is \(40\sqrt{2}\)

and this diagonal will include 2 small circles and 1 large circle so radius of small circle is approx

\(\frac{(40\sqrt{2} - 40)}{2}\)( 40root2-40/2)

so \(20(\sqrt{2}-1)\) (this will be a bit bigger than diameter of smaller circle)

we need radius then divide it by 2 which make bit bigger than radius as \(10(\sqrt{2}-1)\)

but as you can see both small circles are not touching in the corner of the square then the answer will be little less than the above answer

above answer in terms of value is 10*0.3=3 correct answer will be little less

A.10*0.3= 3 our answer were bith less than 3

B.6 way greater than 3 incorrect

C.6/2.3= 2.3 (bit less correct)

D.40*0.3= 12 (very large)

E.40*0.3/2.3= 5.3(greater than 3 incorrect)

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