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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2011 China Second Round Olympiad
6
6
Part of
2011 China Second Round Olympiad
Problems
(1)
radius of a circumsphere
Source: China Second Round Test1
1/30/2012
In a tetrahedral
A
B
C
D
ABCD
A
BC
D
, given that
∠
A
D
B
=
∠
B
D
C
=
∠
C
D
A
=
π
3
\angle ADB=\angle BDC =\angle CDA=\frac{\pi}{3}
∠
A
D
B
=
∠
B
D
C
=
∠
C
D
A
=
3
π
,
A
D
=
B
D
=
3
AD=BD=3
A
D
=
B
D
=
3
, and
C
D
=
2
CD=2
C
D
=
2
. Find the radius of the circumsphere of
A
B
C
D
ABCD
A
BC
D
.
analytic geometry
trigonometry
geometry
3D geometry
tetrahedron
geometry unsolved