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France Contests
French Mathematical Olympiad
1989 French Mathematical Olympiad
Problem 3
Problem 3
Part of
1989 French Mathematical Olympiad
Problems
(1)
tetrahedron inequality, with parameter
Source: France 1989 P3
5/18/2021
Find the greatest real
k
k
k
such that, for every tetrahedron
A
B
C
D
ABCD
A
BC
D
of volume
V
V
V
, the product of areas of faces
A
B
C
,
A
B
D
ABC,ABD
A
BC
,
A
B
D
and
A
C
D
ACD
A
C
D
is at least
k
V
2
kV^2
k
V
2
.
geometry
3D geometry
tetrahedron
inequalities
geometric inequality
Geometric Inequalities