Circles and Squares

Geometry Level pending

A circle with a radius of 2 has a chord $$AB$$ of 2. A square with a side $$AB$$ is constructed, leaving the two other vertices outside the circle. If the total area of the figure can be expressed as $$\frac{a\pi}{b}+\sqrt{c}+d$$, where a and b are relatively prime, what is $$a+b+c+d$$?

Note: $$A$$ is not equal to $$a$$, and $$B$$ is not equal to $$b$$

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