Overleg:Gelijke-omweg-punt
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The condition is actually not true. A counter example for instance is a triangle with which has 2 points with the equal detour property despite the inequality holding. See also:
- M. Hajja, P. Yff: "The isoperimetric point and the point(s) of equal detour in a triangle". Journal of Geometry,November 2007, Volume 87, Issue 1–2, pp 76–82, https://doi.org/10.1007/s00022-007-1906-y