https://artofproblemsolving.com/wiki/index.php?title=2006_IMO_Problems/Problem_6&feed=atom&action=history 2006 IMO Problems/Problem 6 - Revision history 2021-07-31T08:29:12Z Revision history for this page on the wiki MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=2006_IMO_Problems/Problem_6&diff=62103&oldid=prev Swamih: Created page with "==Problem== Assign to each side [itex]b[/itex] of a convex polygon [itex]P[/itex] the maximum area of a triangle that has [itex]b[/itex] as a side and is contained in [itex]P</ma..." 2014-05-23T03:15:12Z <p>Created page with &quot;==Problem== Assign to each side &lt;math&gt;b&lt;/math&gt; of a convex polygon &lt;math&gt;P&lt;/math&gt; the maximum area of a triangle that has &lt;math&gt;b&lt;/math&gt; as a side and is contained in &lt;math&gt;P&lt;/ma...&quot;</p> <p><b>New page</b></p><div>==Problem==<br /> Assign to each side &lt;math&gt;b&lt;/math&gt; of a convex polygon &lt;math&gt;P&lt;/math&gt; the maximum area of a triangle that has &lt;math&gt;b&lt;/math&gt; as a side and is contained in &lt;math&gt;P&lt;/math&gt;. Show that the sum of the areas assigned to the sides of &lt;math&gt;P&lt;/math&gt; is at least twice the area of &lt;math&gt;P&lt;/math&gt;.<br /> <br /> ==Solution==<br /> .</div> Swamih