Overleg:Gelijke-omweg-punt

The condition $max(\alpha ,\beta ,\gamma )\leq 2\arcsin(0.8)$ is actually not true. A counter example for instance is a triangle with $\alpha =74.71^{\circ },\beta =1.78^{\circ },\gamma =103.51^{\circ }$ 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

--Kmhkmh (overleg) 8 feb 2020 14:29 (CET)