Difference between revisions of "2006 IMO Problems/Problem 6"
Akshjuneja (talk | contribs) |
Mathhyhyhy (talk | contribs) (→Problem) |
||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
==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>. | ||
| + | |||
| + | |||
==Solution== | ==Solution== | ||
| − | |||
==See Also== | ==See Also== | ||
{{IMO box|year=2006|num-b=5|after=Last Problem}} | {{IMO box|year=2006|num-b=5|after=Last Problem}} | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
Latest revision as of 03:20, 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 | ||
