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Manhattan Prep
ABCD is a square inscribed in a circle and arc ADC has a length of \(\pi\sqrt{x}.\) If a dart is thrown and lands somewhere in the circle, what is the probability that it will not fall within the inscribed square? (Assume that the point in the circle where the dart lands is completely random.)
A. \(2x\)
B. \(\pi(x)-2x\)
C. \(\pi(x)-\sqrt{2}(x)\)
D. \(1-\frac{2}{\pi}\)
E. \(1-\frac{2}{x}\)
OA D
A. \(2x\)
B. \(\pi(x)-2x\)
C. \(\pi(x)-\sqrt{2}(x)\)
D. \(1-\frac{2}{\pi}\)
E. \(1-\frac{2}{x}\)
OA D