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Saint Petersburg Mathematical Olympiad
2001 Saint Petersburg Mathematical Olympiad
10.5
10.5
Part of
2001 Saint Petersburg Mathematical Olympiad
Problems
(1)
Find angle AMN
Source: St. Petersburg MO 2001, 10th grade P5
4/24/2023
On the bisector
A
L
AL
A
L
of triangle
A
B
C
ABC
A
BC
a point
K
K
K
is chosen such that
∠
B
K
L
=
∠
K
B
L
=
3
0
∘
\angle BKL=\angle KBL=30^{\circ}
∠
B
K
L
=
∠
K
B
L
=
3
0
∘
. Lines
A
B
AB
A
B
and
C
K
CK
C
K
intersect at point
M
M
M
, lines
A
C
AC
A
C
and
B
K
BK
B
K
intersect at point
N
N
N
. FInd the measure of angle
∠
A
M
N
\angle AMN
∠
A
MN
[I]Proposed by D. Shiryaev, S. Berlov
geometry
angle
bisector