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Mexico National Olympiad
2007 Mexico National Olympiad
3
Midpoint and Strange Point
Midpoint and Strange Point
Source: OMM 2007 6
July 19, 2014
geometry unsolved
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
>
B
C
>
C
A
AB>BC>CA
A
B
>
BC
>
C
A
. Let
D
D
D
be a point on
A
B
AB
A
B
such that
C
D
=
B
C
CD=BC
C
D
=
BC
, and let
M
M
M
be the midpoint of
A
C
AC
A
C
. Show that
B
D
=
A
C
BD=AC
B
D
=
A
C
and that
∠
B
A
C
=
2
∠
A
B
M
.
\angle BAC=2\angle ABM.
∠
B
A
C
=
2∠
A
BM
.
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