## Πέμπτη, 12 Οκτωβρίου 2017

### 1997 JBMO problem 3 (GRE)

proposed by Greece

Let ${ABC }$  be a triangle and let ${I }$  be the incenter. Let ${N, M }$  be the midpoints of the sides ${AB }$  and ${CA }$  respectively. The lines ${BI }$  and ${CI }$  meet ${MN }$  at ${K }$  and ${L }$  respectively. Prove that ${AI + BI + CI > BC + KL }$.

posted in aops here