An arbitrary point $M$ is chosen inside the triangle $ABC$. Prove that $MA + MB + MC \le max (AB + BC, BC + AC, AC + AB)$. (N. Sedrakyan)
Problem
Source: 2005 Oral Moscow Geometry Olympiad grades 10-11 p5
Tags: geometry, geometric inequality
Source: 2005 Oral Moscow Geometry Olympiad grades 10-11 p5
Tags: geometry, geometric inequality
An arbitrary point $M$ is chosen inside the triangle $ABC$. Prove that $MA + MB + MC \le max (AB + BC, BC + AC, AC + AB)$. (N. Sedrakyan)