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>. | ||
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| − | <math>MERLIN</math> | + | |
| + | <math>MERLIN</math> 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 10:18, 7 June 2024
Problem
Assign to each side 
of a convex polygon 
the maximum area of a triangle that has as a side and is contained in . Show that the sum of the areas assigned to the sides of is at least twice the area of .
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 | ||
