MathDB
Problems
Contests
International Contests
Baltic Way
1994 Baltic Way
14
14
Part of
1994 Baltic Way
Problems
(1)
Ienquality involving sides a,b,c and angles α, β, γ
Source: Baltic Way 1994
12/22/2011
Let
α
,
β
,
γ
\alpha,\beta,\gamma
α
,
β
,
γ
be the angles of a triangle opposite to its sides with lengths
a
,
b
,
c
a,b,c
a
,
b
,
c
respectively. Prove the inequality
a
(
1
β
+
1
γ
)
+
b
(
1
γ
+
1
α
)
+
c
(
1
α
+
1
β
)
≥
2
(
a
α
+
b
β
+
c
γ
)
a\left(\frac{1}{\beta}+\frac{1}{\gamma}\right)+b\left(\frac{1}{\gamma}+\frac{1}{\alpha}\right)+c\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)\ge2\left(\frac{a}{\alpha}+\frac{b}{\beta}+\frac{c}{\gamma}\right)
a
(
β
1
+
γ
1
)
+
b
(
γ
1
+
α
1
)
+
c
(
α
1
+
β
1
)
≥
2
(
α
a
+
β
b
+
γ
c
)
geometry unsolved
geometry
Inequality