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2011 Kyrgyzstan National Olympiad
5
Geo Problem(KgNM2011)
Geo Problem(KgNM2011)
Source:
April 20, 2011
geometry unsolved
geometry
Problem Statement
Points
M
M
M
and
N
N
N
are chosen on sides
A
B
AB
A
B
and
B
C
BC
BC
,respectively, in a triangle
A
B
C
ABC
A
BC
, such that point
O
O
O
is interserction of lines
C
M
CM
CM
and
A
N
AN
A
N
. Given that
A
M
+
A
N
=
C
M
+
C
N
AM+AN=CM+CN
A
M
+
A
N
=
CM
+
CN
. Prove that
A
O
+
A
B
=
C
O
+
C
B
AO+AB=CO+CB
A
O
+
A
B
=
CO
+
CB
.
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