Geodesic
On affine diameters and chords of convex compacta
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 252-261
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Existence theorems are proved for collections of affine diameters of a convex body that satisfy various additional conditions. The area of a convex planar figure is estimated via the maximal length of a chord dividing the area of the figure in a given ratio. 
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V. V. Makeev. On affine diameters and chords of convex compacta. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 252-261. http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a15/

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