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2022 Polish Junior Math Olympiad Finals
1.
1.
Part of
2022 Polish Junior Math Olympiad Finals
Problems
(1)
2022 Polish Junior Math Olympiad Finals P1
Source: 2022 Polish Junior Math Olympiad Finals P1
5/21/2023
Given is a square
A
B
C
D
ABCD
A
BC
D
with side length
1
1
1
. Points
K
K
K
,
L
L
L
,
M
M
M
, and
N
N
N
, distinct from the vertices of the square, lie on segments
A
B
AB
A
B
,
B
C
BC
BC
,
C
D
CD
C
D
, and
D
A
DA
D
A
, respectively. Prove that the perimeter of at least one of the triangles
A
N
K
ANK
A
N
K
,
B
K
L
BKL
B
K
L
,
C
L
M
CLM
C
L
M
,
D
M
N
DMN
D
MN
is less than
2
2
2
.
geometry