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2010 Paraguay Mathematical Olympiad
3
Paraguayan National Olympiad 2010, Level 3, Problem 3
Paraguayan National Olympiad 2010, Level 3, Problem 3
Source:
September 20, 2014
Problem Statement
In a triangle
A
B
C
ABC
A
BC
, let
M
M
M
be the midpoint of
A
C
AC
A
C
. If
B
C
=
2
3
M
C
BC = \frac{2}{3} MC
BC
=
3
2
MC
and
∠
B
M
C
=
2
∠
A
B
M
\angle{BMC}=2 \angle{ABM}
∠
BMC
=
2∠
A
BM
, determine
A
M
A
B
\frac{AM}{AB}
A
B
A
M
.
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