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Problems
Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
1998 Greece National Olympiad
2
2
Part of
1998 Greece National Olympiad
Problems
(1)
Sum of squares of segments is greater than twice the area
Source: Greece MO 1998
5/27/2011
For a regular
n
n
n
-gon, let
M
M
M
be the set of the lengths of the segments joining its vertices. Show that the sum of the squares of the elements of
M
M
M
is greater than twice the area of the polygon.
geometry
rectangle
geometry proposed