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Baltic Way
1997 Baltic Way
14
14
Part of
1997 Baltic Way
Problems
(1)
2b^2=a^2+c^2 in triangle ABC inequality
Source: Baltic Way 1997
1/28/2011
In the triangle
A
B
C
ABC
A
BC
,
A
C
2
AC^2
A
C
2
is the arithmetic mean of
B
C
2
BC^2
B
C
2
and
A
B
2
AB^2
A
B
2
. Show that
cot
2
B
≥
cot
A
⋅
cot
C
\cot^2B\ge \cot A\cdot\cot C
cot
2
B
≥
cot
A
⋅
cot
C
.
inequalities
trigonometry
geometry
geometry proposed