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Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
1969 Canada National Olympiad
3
3
Part of
1969 Canada National Olympiad
Problems
(1)
Hypotenuse inequality
Source:
5/14/2006
Let
c
c
c
be the length of the hypotenuse of a right angle triangle whose two other sides have lengths
a
a
a
and
b
b
b
. Prove that
a
+
b
≤
c
2
a+b\le c\sqrt{2}
a
+
b
≤
c
2
. When does the equality hold?
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