Abstract
This paper gives a partial answer to a problem posed by Volcic and shows, in particular, that a three-dimensional convex body K is uniquely determined if p ′ and p ″ are two points interior to K and the lengths of all the chords of K through p ′ and the areas of all sections of K with planes through p ″ are known, provided that a specific condition on the positions of p ′ and p ″ with respect to K is satisfied. The problem will be studied in the more general framework of i -chord functions, and the results will also cover cases where the points p ′ and p ″ are not interior to K , possibly with one of them at infinity.
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