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International Mathematical Arhimede Contest (IMAC)
2008 IMAC Arhimede
4
4
Part of
2008 IMAC Arhimede
Problems
(1)
calculate cosa in a tetrahedron, related to 2 midpoints
Source: IMAC Arhimede 2008 p4
5/4/2019
Let
A
B
C
D
ABCD
A
BC
D
be a random tetrahedron. Let
E
E
E
and
F
F
F
be the midpoints of segments
A
B
AB
A
B
and
C
D
CD
C
D
, respectively. If the angle
a
a
a
is between
A
D
AD
A
D
and
B
C
BC
BC
, determine
c
o
s
a
cos a
cos
a
in terms of
E
F
,
A
D
EF, AD
EF
,
A
D
and
B
C
BC
BC
.
geometry
3D geometry
tetrahedron
midpoints
trigonometry