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IMC
2002 IMC
10
10
Part of
2002 IMC
Problems
(1)
IMC 2002 Problem 10
Source: IMC 2002 Day 2 Problem 4
10/27/2020
Let
O
A
B
C
OABC
O
A
BC
be a tetrahedon with
∠
B
O
C
=
α
,
∠
C
O
A
=
β
\angle BOC=\alpha,\angle COA =\beta
∠
BOC
=
α
,
∠
CO
A
=
β
and
∠
A
O
B
=
γ
\angle AOB =\gamma
∠
A
OB
=
γ
. The angle between the faces
O
A
B
OAB
O
A
B
and
O
A
C
OAC
O
A
C
is
σ
\sigma
σ
and the angle between the faces
O
A
B
OAB
O
A
B
and
O
B
C
OBC
OBC
is
ρ
\rho
ρ
. Show that
γ
>
β
cos
σ
+
α
cos
ρ
\gamma > \beta \cos\sigma + \alpha \cos\rho
γ
>
β
cos
σ
+
α
cos
ρ
.
3D geometry
tetrahedron
inequalities