Difference between revisions of "1997 JBMO Problems/Problem 3"

(Created page with "== Problem == == Solution == == See also == {{JBMO box|year=1997|num-b=2|num-a=4}}")
 
(Problem)
Line 1: Line 1:
 
== Problem ==
 
== Problem ==
 +
 +
''(Greece)'' Let <math>ABC</math> be a triangle and let <math>I</math> be the incenter. Let <math>N</math>, <math>M</math> be the midpoints of the sides <math>AB</math> and <math>CA</math> respectively. The lines <math>BI</math> and <math>CI</math> meet <math>MN</math> at <math>K</math> and <math>L</math> respectively. Prove that <math>AI+BI+CI>BC+KL</math>.
  
 
== Solution ==
 
== Solution ==

Revision as of 18:21, 15 September 2017

Problem

(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 $AI+BI+CI>BC+KL$.

Solution

See also

1997 JBMO (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5
All JBMO Problems and Solutions


Invalid username
Login to AoPS