Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2006 IMO Problems/Problem 6

Revision as of 22:15, 22 May 2014 by Swamih (talk | contribs) (Created page with "==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</ma...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2006_IMO_Problems/Problem_6&oldid=62103"