The shaded design shown in the diagram is made by drawing eight circular arcs, all with the same radius. The centres of four arcs are the vertices of the square; the centres of the four touching arcs are the midpoints of the sides of the square. The diagonals of the square have length 1.
What is the exact total length of the border of the shaded design? Give your expression in its simplest form.
Select one option, then click Submit.
2\pi
\frac{5\pi}{2}
3\pi
\frac{7\pi}{2}
4\pi
Select an option, then submit.
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