If a circle with a circumference of 16 times pi inches is circumscribed about a square, what is the length of a diagonal of the square?

[4haz]

If a circle with a circumference of 16 times pi inches is circumscribed about a square, what is the length of a diagonal of the square?

 

[mmm4444bot]

Hello. Did you start by drawing a diagram? Please share your beginning efforts, per the forum's guidelines.

Hint: Due to symmetry, when a circle circumscribes a square, each diagonal (of the square) is the same as the circle's diameter.
[imath]\;[/imath]

 

[BigBeachBanana]

 

[MathTutorPro]

Not sure if @4haz is confident with the problem. I would recommend logically reasoning that the diameter of the circle will be the same as the diagonal of the square. Also, remember that Circumference = [imath]\pi[/imath]D