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1970 IMO Longlists
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31
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1970 IMO Longlists
Problems
(1)
An old geometric inequality - appeared on ILL 1970, P31
Source:
5/21/2011
Prove that for any triangle with sides
a
,
b
,
c
a, b, c
a
,
b
,
c
and area
P
P
P
the following inequality holds:
P
≤
3
4
(
a
b
c
)
2
/
3
.
P \leq \frac{\sqrt 3}{4} (abc)^{2/3}.
P
≤
4
3
(
ab
c
)
2/3
.
Find all triangles for which equality holds.
inequalities
geometry