Problem

Source: Tuymaada Mathematical Olympiad 2005, Day 1, Problem 4

Tags: inequalities, geometry, trigonometry, 3D geometry, tetrahedron, triangle inequality, geometry unsolved



In a triangle $ABC$, let $A_{1}$, $B_{1}$, $C_{1}$ be the points where the excircles touch the sides $BC$, $CA$ and $AB$ respectively. Prove that $A A_{1}$, $B B_{1}$ and $C C_{1}$ are the sidelenghts of a triangle. Proposed by L. Emelyanov