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fitzpratik
Two squares are oriented with respect to a circle as shown in the figure. The circle touches all the sides of the larger square and all the angles of the smaller square lie on the circumference of the circle. What is the ratio of the area of the smaller square to that of the larger square is:





A. 1:3

B. 1:4

C. 2:1

D. 1:5

E. 1:2


fitzpratik, it is visible now.

So if we consider the circle of radius 2, then the smaller square will have side as 2\(\sqrt{2}\), since it is a square so the center angle will be a \(90^0\) that will make a 45-45-90 triangle

Now the bigger square will have side as 4, since the circle's diameter = square's side

Area of smaller square / Area of bigger square = 8/16

E
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fitzpratik
Two squares are oriented with respect to a circle as shown in the figure. The circle touches all the sides of the larger square and all the angles of the smaller square lie on the circumference of the circle. What is the ratio of the area of the smaller square to that of the larger square is:





A. 1:3

B. 1:4

C. 2:1

D. 1:5

E. 1:2


the diameter of the circle will be equal to the side of the large square ; let it be = 4
and the diagonal of the small circle equal to diameter of circle ; so d = s√2 ; 4 =s√2 ; side of small square = 2 √2

so area of small square/ area of large square ; 2 *2 * 2 / 4 * 4 ; 1:2 IMO E
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