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May 16, 2013 at 18:16 comment added Nikita Kalinin yes sure. Triangle with sides equal $d$. Its diameter is $d$, its area is $\sqrt{3}d^2/4$. But any figure spanned on two intervals of length $d$ and angle $\pi/3$ between them works as well.
May 15, 2013 at 22:06 comment added alvarezpaiva Do you get the equality case this way?
May 14, 2013 at 21:24 history edited Nikita Kalinin CC BY-SA 3.0
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May 14, 2013 at 21:11 history edited Nikita Kalinin CC BY-SA 3.0
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May 14, 2013 at 15:10 history answered Nikita Kalinin CC BY-SA 3.0