# Circle Areas

Bert Bates

author

Sheriff

Sheriff

Posts: 8900

5

posted 12 years ago

Imagine a circle:

Now imagine a square inside the circle, such that all four of the square's corners touch the edge of the circle (inscribed).

Now imagine a second circle inside the square,such that the inner circle touches the square at all four of the square's midpoints (inscribed).

What's the ratio of areas of the two circles?

Now imagine a square inside the circle, such that all four of the square's corners touch the edge of the circle (inscribed).

Now imagine a second circle inside the square,such that the inner circle touches the square at all four of the square's midpoints (inscribed).

What's the ratio of areas of the two circles?

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posted 12 years ago

I get 2:1

If the square has a length of 2x, then the inner circle has a radius of x and the outer circle a radius of x*sqrt(2). Apply A = PI * r^2 to each circle, and you get areas of PI * x^2 and * PI * x^2, respectively. Reduce (and express in terms of larger:smaller), and you get 2:1.

[ November 16, 2003: Message edited by: Joel McNary ]

If the square has a length of 2x, then the inner circle has a radius of x and the outer circle a radius of x*sqrt(2). Apply A = PI * r^2 to each circle, and you get areas of PI * x^2 and * PI * x^2, respectively. Reduce (and express in terms of larger:smaller), and you get 2:1.

[ November 16, 2003: Message edited by: Joel McNary ]

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