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1993 Poland - First Round
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Part of
1993 Poland - First Round
Problems
(1)
Inequality between the lengths of the sides of a triangle
Source: Poland Math Olympiad 1993 Round 1 #3
6/3/2023
Prove that if
a
,
b
,
c
a,b,c
a
,
b
,
c
are the lengths of the sides of a triangle, then
1
a
+
1
b
+
1
c
≤
1
a
+
b
−
c
+
1
c
+
a
−
b
+
1
b
+
c
−
a
\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \leq \frac{1}{a+b-c}+\frac{1}{c+a-b}+\frac{1}{b+c-a}
a
1
+
b
1
+
c
1
≤
a
+
b
−
c
1
+
c
+
a
−
b
1
+
b
+
c
−
a
1
.
inequalities