Basic Geometry
(Northern Kentucky University)
The square shown below has a side length of 6 inches and is inscribed in a circle so that each vertex of the square lies on the circle. What is the radius of the circle in inches?

Draw radii from the center to each of two adjacent corners to obtain a right triangle with two sides of length r and hypotenuse of length 6. The Pythagorean theorem provides the equation 2r2 = 36, so .