RE: LeoThread 2025-01-06 08:15

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.

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 .

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

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}.

Final Answer:

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