The question is :
"Let $A$ and $B$ be two fixed points in $\mathbb{R}^{2}$. Given $L>$ length of $AB$. Show that the curve $\alpha$ joining A and B, with length $L$, which together with AB forms a Jordan curve (i.e. a simple closed curve), bounds the largest possible area is an arc of a circle passing through $A$ and $B$."
This is an homework question from a Differential Geometry Course.
It seems that it is related to isoperimetric inequality but I don't have any idea to prove it.
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user134927
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Is the proof of the isoperimetric inequality covered in your class? Are you expected to imitate that proof in your exercise? – hardmath Sep 16 '14 at 14:13
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Yes, the lecturer use a theorem in Fourier analysis.It required the boundary is smooth. – user134927 Sep 16 '14 at 14:16
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It makes sense that in a course on Differential Geometry you would assume smoothness of the curve $\alpha$. I think $\mathscr{C}^1$ smoothness is sufficient here. – hardmath Sep 16 '14 at 14:49