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9
2006 SMT Team Round #9 - Geometry
2006 SMT Team Round #9 - Geometry
Source:
August 22, 2011
geometry
Pythagorean Theorem
Problem Statement
△
A
B
C
\triangle ABC
△
A
BC
has
A
B
=
A
C
AB=AC
A
B
=
A
C
. Points
M
M
M
and
N
N
N
are midpoints of
A
B
‾
\overline{AB}
A
B
and
A
C
‾
\overline{AC}
A
C
, respectively. The medians
M
C
‾
\overline{MC}
MC
and
N
B
‾
\overline{NB}
NB
intersect at a right angle. Find
(
A
B
B
C
)
2
(\tfrac{AB}{BC})^2
(
BC
A
B
)
2
.
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