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3
RMT 2015 Geometry #3
RMT 2015 Geometry #3
Source:
October 28, 2022
geometry
3D geometry
Problem Statement
Consider a triangular pyramid
A
B
C
D
ABCD
A
BC
D
with equilateral base
A
B
C
ABC
A
BC
of side length
1
1
1
.
A
D
=
B
D
=
C
D
AD = BD =CD
A
D
=
B
D
=
C
D
and
∠
A
D
B
=
∠
B
D
C
=
∠
A
D
C
=
9
0
o
\angle ADB = \angle BDC = \angle ADC = 90^o
∠
A
D
B
=
∠
B
D
C
=
∠
A
D
C
=
9
0
o
. Find the volume of
A
B
C
D
ABCD
A
BC
D
.
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