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Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1996 Moldova Team Selection Test
7
7
Part of
1996 Moldova Team Selection Test
Problems
(1)
dihedral angle between the planes $(MA_1C)$ and $(NA_1C)$
Source: Moldova TST 1996
8/8/2023
Let
A
B
C
D
A
1
B
1
C
1
D
1
ABCDA_1B_1C_1D_1
A
BC
D
A
1
B
1
C
1
D
1
be a cube. On the sides
A
B
AB{}
A
B
and
A
D
AD{}
A
D
there are the points
M
M{}
M
and
N
N{}
N
, respectively, such that
A
M
+
A
N
=
A
B
AM+AN=AB
A
M
+
A
N
=
A
B
. Show that the measure of the dihedral angle between the planes
(
M
A
1
C
)
(MA_1C)
(
M
A
1
C
)
and
(
N
A
1
C
)
(NA_1C)
(
N
A
1
C
)
doe not depend on the positions of
M
M{}
M
and
N
N{}
N
. Find this measure.
geometry
3D geometry