Is it a segment?

Calculus Level 4

The figure at right shows a unit semicircle (in blue) and the graph of \(f(x)=x+1\) (in green).

Let the purple line segment \(AB\) be the longest vertical line segment that joins the blue semicircle and green line in the domain \([-1,0].\)

If \(R\) is the area of the black shaded region, what is \(\left\lfloor 100R \right\rfloor ?\)

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