Convex solids with hyperplanar midsurfaces for restricted families of chords (Q2883527)

A new characteristic property of convex quadric hypersurfaces (convex quadrics) in~\(\mathbb R^n\) is obtained in terms of hyperplanarity of midsurfaces of convex solids (\(n\)-dimensional closed convex sets distinct from~\(\mathbb R^n\)) for restricted families of chords. These properties are based on various auxiliary characterizations of convex quadrics that involve hyperplane supports and plane quadric sections.