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1987 IMO Shortlist
4
4
Part of
1987 IMO Shortlist
Problems
(1)
Geometric ineq. (IMO SL 1987-P4)
Source:
8/19/2010
Let
A
B
C
D
E
F
G
H
ABCDEFGH
A
BC
D
EFG
H
be a parallelepiped with
A
E
∥
B
F
∥
C
G
∥
D
H
AE \parallel BF \parallel CG \parallel DH
A
E
∥
BF
∥
CG
∥
DH
. Prove the inequality
A
F
+
A
H
+
A
C
≤
A
B
+
A
D
+
A
E
+
A
G
.
AF + AH + AC \leq AB + AD + AE + AG.
A
F
+
A
H
+
A
C
≤
A
B
+
A
D
+
A
E
+
A
G
.
In what cases does equality hold?Proposed by France.
geometry
geometric inequality
3D geometry
polyhedron
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