Difference between revisions of "2006 IMO Problems/Problem 6"
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==Problem== | ==Problem== | ||
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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==Solution== | ==Solution== | ||
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==See Also== | ==See Also== | ||
{{IMO box|year=2006|num-b=5|after=Last Problem}} | {{IMO box|year=2006|num-b=5|after=Last Problem}} | ||
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Latest revision as of 04:20, 31 August 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
.
Solution
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 |