Question 1116523
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The drawing for this situation is:

{{{ drawing(300,300,-5,5,-5,5, grid(0),
                       line(-4,-4,-4,4),
                       line(-4,4,4,4),
                       line(4,4,4,-4),
                       line(4,-4,-4,-4),
                      green(line(-2.8,-2.8,-2.8, 2.8)),
                      green(line(-2.8,2.8,2.8, 2.8)),
                      green(line(2.8,2.8,2.8,-2.8)),
                      green(line(2.8,-2.8,-2.8, -2.8)),  
                      circle(0,0,4)

)
}}}

Let d=diameter of the circle.
The small square has a diagonal length of  d, so the sides are {{{ d/sqrt(2) }}} units long.
The large square has sides that are {{{ d }}} units long.

So the ratio of large to small is   {{{ (d^2)/ ((d^2/2)) = highlight( 2 / 1 )  }}}  or  {{{ highlight( 2:1 ) }}}

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What tutor greenestamps says is correct.  If one draws the inner square as below, the 2:1 ratio in the areas is much more obvious. 


{{{ drawing(300,300,-5,5,-5,5, grid(0),
                       line(-4,-4,-4,4),
                       line(-4,4,4,4),
                       line(4,4,4,-4),
                       line(4,-4,-4,-4),
                      green(line(-4,0,0,4)),
                      green(line(0,4,4,0)),
                      green(line(4,0,0,-4)),
                      green(line(0,-4,-4,0)),  
                      circle(0,0,4)

)
}}}