On the relative distances of eleven points in the boundary of a plane convex body

Let CC be a plane convex body. The relative distance (or CC-distance) of points a,b∈R2a,b∈R2 is defined by the ratio of the Euclidean length of the line-segment abab to half of the Euclidean length of a longest chord of CC, parallel to abab. It was conjectured that there exists no plane convex body whose boundary contains eleven points at pairwise relative distances greater than 23. We give an affirmative answer to this conjecture.