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A9
2008 PUMaC Geometry A9
2008 PUMaC Geometry A9
Source:
November 9, 2012
geometry
3D geometry
tetrahedron
circumcircle
Problem Statement
In tetrahedron
A
B
C
D
ABCD
A
BC
D
with circumradius
2
2
2
,
A
B
=
2
AB = 2
A
B
=
2
,
C
D
=
7
CD = \sqrt{7}
C
D
=
7
, and
∠
A
B
C
=
∠
B
A
D
=
π
2
\angle ABC = \angle BAD = \frac{\pi}{2}
∠
A
BC
=
∠
B
A
D
=
2
π
. Find all possible angles between the planes containing
A
B
C
ABC
A
BC
and
A
B
D
ABD
A
B
D
.
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