Revise your geometry lessons to solve this riddle.
What will be the ratio of the area of the bigger circle to that of the smaller circle in the following figure?
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Let the radius of the small circle be SR &
the radius of the large circle be LR.
Area of small circle = π x SR^2
Area of large circle = π x LR^2
If you see the figure you will notice that the radius of small circle = side of the square &
radius of the large circle = diagonal of the square.
(Diagonal of square)^2 = 2 x (Side)^2
We can write
LR^2 = 2 x SR^2
So we can write;
Area of large circle = π x 2 x SR^2
So the ratio of the areas is 2:1.