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Contests
International Contests
APMO
1996 APMO
5
Triangle inequality
Triangle inequality
Source: APMO 1996
March 12, 2006
inequalities
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
be the lengths of the sides of a triangle. Prove that
a
+
b
−
c
+
b
+
c
−
a
+
c
+
a
−
b
≤
a
+
b
+
c
\sqrt{a+b-c} + \sqrt{b+c-a} + \sqrt{c+a-b} \leq \sqrt{a} + \sqrt{b} + \sqrt{c}
a
+
b
−
c
+
b
+
c
−
a
+
c
+
a
−
b
≤
a
+
b
+
c
and determine when equality occurs.
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