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Problems
Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2014 Sharygin Geometry Olympiad
11
11
Part of
2014 Sharygin Geometry Olympiad
Problems
(1)
Parallel lines inside a square
Source: Sharygin 2014 Correspondence Round
1/8/2015
Points
K
,
L
,
M
K, L, M
K
,
L
,
M
and
N
N
N
lying on the sides
A
B
,
B
C
,
C
D
AB, BC, CD
A
B
,
BC
,
C
D
and
D
A
DA
D
A
of a square
A
B
C
D
ABCD
A
BC
D
are vertices of another square. Lines
D
K
DK
DK
and
N
M
N M
NM
meet at point
E
E
E
, and lines
K
C
KC
K
C
and
L
M
LM
L
M
meet at point
F
F
F
. Prove that
E
F
∥
A
B
EF\parallel AB
EF
∥
A
B
.
geometry unsolved
geometry