Area ratios of squares
Geometry
Level
2
A square is inscribed in a circle. A smaller circle is inscribed in this square. Then a smaller square is inscribed in this smaller circle. Find the ratio of the area of the smaller square to the area of the bigger square.
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1 solution
Imagine the inner square having side length 1 .
By Pythagoras, the diagonal of the square (and hence the diameter of the circle) = 2 .
The area of the large square = side length x side length = diameter x diameter = 2 .
Therefore the answer is 1 : 2