Question 1177019
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Call the center of the circle O.<br>
Let A be the top left corner of the square; let B be the point where the circle is tangent to the right side of the square.<br>
Draw diameter containing OB, intersecting the square at point C, which is the midpoint of that side of the square.<br>
Triangle ACO is a right triangle; leg AC is 2 and the hypotenuse is the radius r of the circle, which is what we are to find.<br>
The length of the other leg CO can be determined in terms of the radius r, knowing that BC is 4 and BO is the radius r.<br>
Use the Pythagorean Theorem to solve to find the radius.<br>