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Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
2001 Mexico National Olympiad
5
5
Part of
2001 Mexico National Olympiad
Problems
(1)
double angle in a triangle given, equal segments wanted
Source: Mexican Mathematical Olympiad 2001 OMM P5
7/30/2018
A
B
C
ABC
A
BC
is a triangle with
A
B
<
A
C
AB < AC
A
B
<
A
C
and
∠
A
=
2
∠
C
\angle A = 2 \angle C
∠
A
=
2∠
C
.
D
D
D
is the point on
A
C
AC
A
C
such that
C
D
=
A
B
CD = AB
C
D
=
A
B
. Let L be the line through
B
B
B
parallel to
A
C
AC
A
C
. Let
L
L
L
meet the external bisector of
∠
A
\angle A
∠
A
at
M
M
M
and the line through
C
C
C
parallel to
A
B
AB
A
B
at
N
N
N
. Show that
M
D
=
N
D
MD = ND
M
D
=
N
D
.
geometry
equal segments