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