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2013 Moldova Team Selection Test
3
Geometric inequality
Geometric inequality
Source: Moldova TST 2013
April 16, 2013
inequalities
trigonometry
inequalities unsolved
Problem Statement
Consider the obtuse-angled triangle
△
A
B
C
\triangle ABC
△
A
BC
and its side lengths
a
,
b
,
c
a,b,c
a
,
b
,
c
. Prove that
a
3
cos
∠
A
+
b
3
cos
∠
B
+
c
3
cos
∠
C
<
a
b
c
a^3\cos\angle A +b^3\cos\angle B + c^3\cos\angle C < abc
a
3
cos
∠
A
+
b
3
cos
∠
B
+
c
3
cos
∠
C
<
ab
c
.
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