Difference between revisions of "2006 IMO Problems/Problem 6"

(Solution)
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{{solution}}
 
{{solution}}
  
<math>MERLIN</math> HAS INFINITE CHARISMA  
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<math>MERLIN</math> HAS INFINITE CHARISMA
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MERLIN IS A SIGMA
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MERLIN IS A SIGMA
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MERLIN IS A SIGMA
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MERLIN IS A SIGMA
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MERLIN IS A SIGMA
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MERLIN IS A SIGMA
  
 
==See Also==
 
==See Also==
  
 
{{IMO box|year=2006|num-b=5|after=Last Problem}}
 
{{IMO box|year=2006|num-b=5|after=Last Problem}}

Revision as of 09:05, 15 May 2024

Problem

Assign to each side $b$ of a convex polygon $P$ the maximum area of a triangle that has $b$ as a side and is contained in $P$. Show that the sum of the areas assigned to the sides of $P$ is at least twice the area of $P$.

Solution

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$MERLIN$ HAS INFINITE CHARISMA MERLIN IS A SIGMA MERLIN IS A SIGMA MERLIN IS A SIGMA MERLIN IS A SIGMA MERLIN IS A SIGMA MERLIN IS A SIGMA

See Also

2006 IMO (Problems) • Resources
Preceded by
Problem 5
1 2 3 4 5 6 Followed by
Last Problem
All IMO Problems and Solutions