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Kosovo MO 2012 Grade 10, Problem 2
Kosovo MO 2012 Grade 10, Problem 2
Source: Kosovo MO 2012 Grade 10, Problem 2
June 7, 2021
geometry
Inequality
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be the lengths of the sides of a triangle. Prove that,
∣
a
b
+
b
c
+
c
a
−
b
a
−
c
b
−
a
c
∣
<
1
\left|\frac {a}{b}+\frac {b}{c}+\frac {c}{a}-\frac {b}{a}-\frac {c}{b}-\frac {a}{c}\right|<1
b
a
+
c
b
+
a
c
−
a
b
−
b
c
−
c
a
<
1
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