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 ${AI + BI + CI > BC + KL }$.

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