The diagram shows four unit circles and two squares. The gray square is formed by the tangency points between the circles. The blue square is formed by joining the midpoints of each arc that are formed by tangency points.
Find the difference of between the area of the gray square and that of the blue square.
+128475 Side of grey square = sqrt (2) units
Area of grey square= (sqrt (2) )^2 = 2
Distance between circle drawn through the diagonal of the square = sqrt (8)
Diagonal of blue square = sqrt (8) - 2
Side of blue square = [ sqrt (8) - 2 ] /sqrt (2)
Area of blue square = (1/2) (sqrt (8) -2)^2 = .343
Difference of areas = 2 - .343 ≈ 1.657 units^2
