Is it a segment?

Calculus Level 4

The figure above shows a unit semicircle (in blue) and \(f(x)=x+1\) (in green).

Let the purple line segment \(AB\) be the longest vertical line segment that joins the blue and green lines 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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