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Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1997 AMC 12/AHSME
25
25
Part of
1997 AMC 12/AHSME
Problems
(1)
A Parallelogram in Space
Source:
1/18/2009
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram and let
A
A
′
→
\overrightarrow{AA^\prime}
A
A
′
,
B
B
′
→
\overrightarrow{BB^\prime}
B
B
′
,
C
C
′
→
\overrightarrow{CC^\prime}
C
C
′
, and
D
D
′
→
\overrightarrow{DD^\prime}
D
D
′
be parallel rays in space on the same side of the plane determined by
A
B
C
D
ABCD
A
BC
D
. If AA^\prime \equal{} 10, BB^\prime \equal{} 8, CC^\prime \equal{} 18, DD^\prime \equal{} 22, and
M
M
M
and
N
N
N
are the midpoints of
A
′
C
′
‾
\overline{A^{\prime}C^{\prime}}
A
′
C
′
and
B
′
D
′
‾
\overline{B^{\prime}D^{\prime}}
B
′
D
′
, respectively, then MN \equal{}
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4
<span class='latex-bold'>(A)</span>\ 0\qquad <span class='latex-bold'>(B)</span>\ 1\qquad <span class='latex-bold'>(C)</span>\ 2\qquad <span class='latex-bold'>(D)</span>\ 3\qquad <span class='latex-bold'>(E)</span>\ 4
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4
geometry
parallelogram