You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square.
Notice that diagonals of the inscribed square are also diameters of circle such that:
`d = 2R`
You need to remember that diagonal of the square is hypotenuse in rigth angle triangle that has the legs equal to x.
Using Pythagorean theorem yields:
`(2R)^2 = x^2 + x^2 =gt 4R^2 = 2x^2 =gt 2R^2 = x^2`
`x = Rsqrt2`
Hence, evaluating the dimensions of the square under given conditions, yields that the length of each side of inscribed square is `x = Rsqrt2 ` and the length of diagonal of the square is `d = 2R` .