# Problem #2180

 2180 A region is bounded by semicircular arcs constructed on the side of a square whose sides measure $\frac{2}{\pi}$, as shown. What is the perimeter of this region? $[asy] unitsize(1cm); defaultpen(.8); filldraw( circle( (0,1), 1 ), lightgray, black ); filldraw( circle( (0,-1), 1 ), lightgray, black ); filldraw( circle( (1,0), 1 ), lightgray, black ); filldraw( circle( (-1,0), 1 ), lightgray, black ); filldraw( (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle, lightgray, black ); [/asy]$ $\mathrm{(A) \ } \frac{4}{\pi}\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } \frac{8}{\pi}\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ } \frac{16}{\pi}$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
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