how do you circumscribe a square about a semicircle with a given radius?

thanks.

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- February 16th 2009, 12:45 AMPabo258circumscribe a square about a semicircle
how do you circumscribe a square about a semicircle with a given radius?

thanks. - February 16th 2009, 01:32 AMearboth
- February 16th 2009, 05:32 AMHallsofIvy
Cute! I notice that actually touches the semi-circle at two points. In what sense does that "circumscribe" the semi-circle better than, say, the square that would circumscribe the entire circle, which touches the semi-circle at three points?

- February 16th 2009, 06:58 AMearboth
That depends on how you define "circumscribe".

As I understand it the**semicircle**has to determine a**square**. If the base line of the semicircle (the diameter of the circle) is parallel to one of the square's side then a square isn't necessary. You can take a rectangle too.

If the base line is tilted less than 45° then the semicircle defines a rectangle too, but the question asks for a square. (Thinking)