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     4 days ago  

    Let’s directly solve this:

    Step 1: Key Observations

    The circle is tangent to all sides of the large square and the smaller squares.

    The center of the circle is at the intersection of the diagonals of the two smaller squares.

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       4 days ago  

      Step 2: Solve for the Circle’s Radius

      1. The large square has a side length of 4 (since ).
      1. The diagonals of each smaller square measure .
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         4 days ago  

        The center of the circle is halfway along this diagonal, so the distance from the center of the smaller square to its corner is .

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           4 days ago  
          1. The radius R is the distance from the center of the circle to a corner of the large square, minus :

          R = 2 - \sqrt{2}.

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             4 days ago  

            Final Answer:

            R = 2 - \sqrt{2} \approx 0.586

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