MathDB
Geometric inequality!

Source: India TST 2001 Day 1 Problem 3

January 31, 2015
inequalitiesgeometryincentergeometry unsolved

Problem Statement

In a triangle ABCABC with incircle ω\omega and incenter II , the segments AIAI , BIBI , CICI cut ω\omega at DD , EE , FF , respectively. Rays AIAI , BIBI , CICI meet the sides BCBC , CACA , ABAB at LL , MM , NN respectively. Prove that: AL+BM+CN≤3(AD+BE+CF)AL+BM+CN \leq 3(AD+BE+CF) When does equality occur?
Back to ProblemsView on AoPS