To have the strip at its maximum height the figure looks like the following
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GRE circles.png [ 2.53 KiB | Viewed 3497 times ]
The circles are connected at the centers thanks to an equilateral triangle
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GRE circles (2).png [ 4.39 KiB | Viewed 3767 times ]
H is the following
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GRE circles (3).png [ 1.63 KiB | Viewed 3795 times ]
so the height is
h=2√3Adding to this the distances on top and at the bottom of the triangle
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GRE circles (4).png [ 4.83 KiB | Viewed 3804 times ]
we do have
4+2√3B is the answer