In traditional Buddhist architecture in Thailand, the square area surrounding the circular-based Chedi (Buddhist shrine) is characteristically modified to assimilate the structure's curvature with a method called "corner reduction 12": each square corner is cut so that 3 new right angles are formed, resulting in 12 angles in total as shown.

If we design the corner angles to touch the red tangents joining the square midpoints, and the smaller sides forming all the new right angles are equal, what is the fraction of the blue area compared to the big square?

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