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ABC be an acute-angled

Source: Indian TST Day 4 Problem 1

June 30, 2011
inequalitiestrigonometryinequalities unsolved

Problem Statement

Let ABCABC be an acute-angled triangle. Let AD,BE,CFAD,BE,CF be internal bisectors with D,E,FD, E, F on BC,CA,ABBC, CA, AB respectively. Prove that EFBC+FDCA+DEAB≥1+rR\frac{EF}{BC}+\frac{FD}{CA}+\frac{DE}{AB}\geq 1+\frac{r}{R}
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