Could anyone find the solution for this generalization for Dido problem: given a big circle island with radius $R$ and line with fixed length $l << R$ we want to find the maximal area bounded by this line and the border of island?
So I've been thinking on this problem for couple of days and haven't solution yet. I think the solution is some arc of circle, but I can't find the maximum of the resulting formula for area (and also Wolfram Mathematica can't, or maybe I do something wrong in it).
Maybe it will be helpful to solve Dido problem for island with angle shape.
Or maybe some Euler-Lagrange equations for this problem are known?