Difference between revisions of "1997 JBMO Problems/Problem 3"
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== Problem == | == Problem == | ||
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| + | ''(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 17:21, 15 September 2017
Problem
(Greece) Let 
be a triangle and let 
be the incenter. Let 
, 
be the midpoints of the sides 
and 
respectively. The lines 
and 
meet 
at 
and 
respectively. Prove that 
.
Solution
See also
| 1997 JBMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All JBMO Problems and Solutions | ||
