the diameter of the circle is the length of the square's diagonal. so half of the square is a right triangle. the pythagorean theorem states, the square of the diagonal is the sum of the squares of the other two sides. so if D is the diagonal and the other two equal sides are A, then D [5] squared = 2 x A squared... 25=2x[AxA] ... [AxA] = 25/2 ... 12.5 = [AxA] ... A = square root of 12.5 ...A = 3.5355". so the inside square is 3.5355"