Geometry Quiz: Find the Ratio of the areas of the Circles

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.

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