Part of circle outside square!

Geometry Level 2

The diagram above shows a circle of diameter 2 touching a vertex of a square of width 2.

Find the minimum possible area of the region of the circle that falls outside of the square.

\cfrac { \pi -1 }{ 4 }

\cfrac { \pi -1 }{ 2 }

\cfrac { \pi }{ 4 }

\cfrac { \pi -2 }{ 2 }

None of these choices