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National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2000 Saint Petersburg Mathematical Olympiad
9.6
9.6
Part of
2000 Saint Petersburg Mathematical Olympiad
Problems
(1)
Two lines concurrent of the external angle bisector.
Source: St. Petersburg MO 2000, 9th grade, P6
4/22/2023
Excircle of
A
B
C
ABC
A
BC
is tangent to the side
B
C
BC
BC
at point
K
K
K
and is tangent to the extension of
A
B
AB
A
B
at point
L
L
L
. Another excircle is tangent to extensions of sides
A
B
AB
A
B
and
B
C
BC
BC
at points
M
M
M
and
N
N
N
. Lines
K
L
KL
K
L
and
M
N
MN
MN
intersect at point
X
X
X
. Prove that
C
X
CX
CX
is the bisector of angle
A
C
N
ACN
A
CN
.[I]Proposed by S. Berlov
geometry
angle bisector