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International Contests
Baltic Way
2002 Baltic Way
14
14
Part of
2002 Baltic Way
Problems
(1)
Angle LNM is a right angle if ∠ALB=∠MNB
Source: Baltic Way 2002
11/13/2010
Let
L
,
M
L,M
L
,
M
and
N
N
N
be points on sides
A
C
,
A
B
AC,AB
A
C
,
A
B
and
B
C
BC
BC
of triangle
A
B
C
ABC
A
BC
, respectively, such that
B
L
BL
B
L
is the bisector of angle
A
B
C
ABC
A
BC
and segments
A
N
,
B
L
AN,BL
A
N
,
B
L
and
C
M
CM
CM
have a common point. Prove that if
∠
A
L
B
=
∠
M
N
B
\angle ALB=\angle MNB
∠
A
L
B
=
∠
MNB
then
∠
L
N
M
=
9
0
∘
\angle LNM=90^{\circ}
∠
L
NM
=
9
0
∘
.
geometry proposed
geometry