Question

Question a square is inscribed in a circle. The same square is also circumscribed about a smaller circle. Find the ratio of the area of the larger circle to the area of the smaller circle

Answer 1

2

Explanation:

You want the ratio of the areas of the circumscribed circle of a square to the inscribed circle of the same square.

Scale factor

The diameter of the inscribed circle is the side length of the square.

The diameter of the circumscribed circle is √2 times the side length of the square.

The ratio of circle areas is the square of the ratio of the diameters:

area scale factor = ((large diameter)/(small diameter))²

area scale factor = ((s√2)/(s))²

area scale factor = 2

The ratio of areas is 2.

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Additional comment

This means the area of the annulus is the same as the area of the inscribed circle.

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