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2005 JBMO Shortlist
3
3
Part of
2005 JBMO Shortlist
Problems
(1)
Regular hexagon
Source: JBMO 2005 Shortlist
10/17/2012
Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a regular hexagon and
M
∈
(
D
E
)
M\in (DE)
M
∈
(
D
E
)
,
N
∈
(
C
D
)
N\in(CD)
N
∈
(
C
D
)
such that
m
(
A
M
N
^
)
=
9
0
∘
m (\widehat {AMN}) = 90^\circ
m
(
A
MN
)
=
9
0
∘
and
A
N
=
C
M
2
AN = CM \sqrt {2}
A
N
=
CM
2
. Find the value of
D
M
M
E
\frac{DM}{ME}
ME
D
M
.
geometry
circumcircle
trigonometry
angle bisector
geometry unsolved