Asquare is inscribed in a circle that has a radius of 2√2 inches. what is the length of the side of the square? -8√2 -8 -4√2 -4

The answer is 4, so it looks like choice D is the answer. However, the -4 should be +4 or just 4. A negative side length does not make any sense.

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Check out the attached image to see everything drawn out. 

Things to notice
* AC is the radius which is 2*sqrt(2). AB and AD are also radii

* BD is the diameter which is double the radius. So the diameter is 4*sqrt(2)

* If you focus on triangle BCD, you'll see a right triangle form. The 90 degree angle is at angle C of triangle BCD. This triangle has BD as the hypotenuse. The diameter of the circle is the hypotenuse of the right triangle. Therefore, the hypotenuse is 4*sqrt(2)

* Based on that fact above, we have a 45-45-90 triangle with a hypotenuse of 4*sqrt(2). It is in the form x*sqrt(2) with x = 4. This is from the special 45-45-90 triangle template. If the legs are x = 4, then the hypotenuse is x*sqrt(2) = 4*sqrt(2).

So that's why the side length of the square is 4. You can also use the Pythagorean theorem (solve x^2+x^2 = (4*sqrt(2))^2 to get the proper value of x) as an alternative method.

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