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Vietnam National Olympiad
1970 Vietnam National Olympiad
1
1
Part of
1970 Vietnam National Olympiad
Problems
(1)
sin A/2 sin B /2 sin C/ 2 < 1/ 4.
Source: Vietnamese MO (VMO) 1970
8/23/2018
Prove that for an arbitrary triangle
A
B
C
ABC
A
BC
:
s
i
n
A
2
s
i
n
B
2
s
i
n
C
2
<
1
4
sin \frac{A}{2} sin \frac{B}{2} sin \frac{C}{2} < \frac{1}{4}
s
in
2
A
s
in
2
B
s
in
2
C
<
4
1
.
trigonometry
Trigonometric inequality
geometry
inequalities