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

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Assign to each side <math>b</math> of a convex polygon <math>P</math> the maximum area of a triangle that has <math>b</math> as a side and is contained in <math>P</math>. Show that the sum of the areas assigned to the sides of <math>P</math> is at least twice the area of <math>P</math>.
 
Assign to each side <math>b</math> of a convex polygon <math>P</math> the maximum area of a triangle that has <math>b</math> as a side and is contained in <math>P</math>. Show that the sum of the areas assigned to the sides of <math>P</math> is at least twice the area of <math>P</math>.
  
==Solution==
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{{solution}}
 
  
 
<math>MERLIN</math> IS A SIGMA
 
<math>MERLIN</math> IS A SIGMA

Revision as of 10:18, 7 June 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 $P$.


$MERLIN$ 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