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Baltic Way
2010 Baltic Way
15
15
Part of
2010 Baltic Way
Problems
(1)
Find angle MXN
Source: Baltic Way 2010
11/19/2010
The points
M
M
M
and
N
N
N
are chosen on the angle bisector
A
L
AL
A
L
of a triangle
A
B
C
ABC
A
BC
such that
∠
A
B
M
=
∠
A
C
N
=
2
3
∘
\angle ABM=\angle ACN=23^{\circ}
∠
A
BM
=
∠
A
CN
=
2
3
∘
.
X
X
X
is a point inside the triangle such that
B
X
=
C
X
BX=CX
BX
=
CX
and
∠
B
X
C
=
2
∠
B
M
L
\angle BXC=2\angle BML
∠
BXC
=
2∠
BM
L
. Find
∠
M
X
N
\angle MXN
∠
MXN
.
geometry
circumcircle
angle bisector
geometry proposed