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[Solved] Finding the radius of the circle

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Draw diagonal QS and notice that it is also a diameter of the circle. Each triangle formed is an isosceles (45-45-90) right triangle, so the sides of \small \Delta QRS are in the ratio \small 1:1:\sqrt{2}.  The area of the square is 4, so each side of the square is 2, and the sides of  \small \Delta QRS are 2, 2 and \small 2\sqrt{2}.  (Multiply all numbers in the ratio \small 1:1:\sqrt{2}  by 2 to get the ratio \small 2:2:2\sqrt{2}.)   So   \small SQ=2\sqrt{2},  and the radius is half that: \small \frac{1}{2}*2\sqrt{2}=\sqrt{2}.

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