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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2023 All-Russian Olympiad Regional Round
10.8
10.8
Part of
2023 All-Russian Olympiad Regional Round
Problems
(1)
Equal segments in a parallelogram
Source: ARO Regional stage 2023 10.8
2/16/2023
The bisector of
∠
B
A
D
\angle BAD
∠
B
A
D
of a parallelogram
A
B
C
D
ABCD
A
BC
D
meets
B
C
BC
BC
at
K
K
K
. The point
L
L
L
lies on
A
B
AB
A
B
such that
A
L
=
C
K
AL=CK
A
L
=
C
K
. The lines
A
K
AK
A
K
and
C
L
CL
C
L
meet at
M
M
M
. Let
(
A
L
M
)
(ALM)
(
A
L
M
)
meet
A
D
AD
A
D
after
D
D
D
at
N
N
N
. Prove that
∠
C
N
L
=
9
0
o
\angle CNL=90^{o}
∠
CN
L
=
9
0
o
geometry
parallelogram
Russia