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Canada Contests
Canada National Olympiad
1970 Canada National Olympiad
5
5
Part of
1970 Canada National Olympiad
Problems
(1)
Quadrilateral inside square
Source: Canada 1970, Problem 5
5/14/2006
A quadrilateral has one vertex on each side of a square of side-length 1. Show that the lengths
a
a
a
,
b
b
b
,
c
c
c
and
d
d
d
of the sides of the quadrilateral satisfy the inequalities
2
≤
a
2
+
b
2
+
c
2
+
d
2
≤
4.
2\le a^2+b^2+c^2+d^2\le 4.
2
≤
a
2
+
b
2
+
c
2
+
d
2
≤
4.
inequalities