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1986 IMO Shortlist
19
19
Part of
1986 IMO Shortlist
Problems
(1)
Compute the least value of f(p) - ISL 1986
Source:
8/31/2010
A tetrahedron
A
B
C
D
ABCD
A
BC
D
is given such that
A
D
=
B
C
=
a
;
A
C
=
B
D
=
b
;
A
B
ā
C
D
=
c
2
AD = BC = a; AC = BD = b; AB\cdot CD = c^2
A
D
=
BC
=
a
;
A
C
=
B
D
=
b
;
A
B
ā
C
D
=
c
2
. Let
f
(
P
)
=
A
P
+
B
P
+
C
P
+
D
P
f(P) = AP + BP + CP + DP
f
(
P
)
=
A
P
+
BP
+
CP
+
D
P
, where
P
P
P
is an arbitrary point in space. Compute the least value of
f
(
P
)
.
f(P).
f
(
P
)
.
geometry
3D geometry
tetrahedron
circumcircle
IMO Shortlist
minimization