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2014 Portugal MO
2
FINALS - Portuguese Mathematical Olympiad (High-School) P2
FINALS - Portuguese Mathematical Olympiad (High-School) P2
Source:
April 6, 2014
geometry unsolved
geometry
Problem Statement
Let
[
A
B
C
D
]
[ABCD]
[
A
BC
D
]
be a square,
M
M
M
a point on the segment
[
A
D
]
[AD]
[
A
D
]
, and
N
N
N
a point on the segment
[
D
C
]
[DC]
[
D
C
]
such that
B
M
^
A
=
N
M
^
D
=
6
0
ā
B\hat{M}A = N\hat{M}D = 60^{\circ}
B
M
^
A
=
N
M
^
D
=
6
0
ā
. Calculate
M
B
^
N
M\hat{B}N
M
B
^
N
.
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