Chapter 6 - Section 6.2 - More Angle Measures in the Circle - Exercises - Page 299: 37

.83

First, we know that the radius of the larger circle is equal to 4 cm, since this is the length of the side of a square. We now find the length of the diagonal of the square. This is a 45-45-90 triangle, so its length is: $4 \sqrt2 = 5.66$. We know the diameter equals half the difference between these two, so we find: $ d = 1/2(5.66 - 4) = .83$