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National and Regional Contests
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Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2020.7.4
2020.7.4
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
2 equal rectangles inscribed in square (2020 Kyiv City MO 7.4)
Source:
9/19/2020
Given a square
A
B
C
D
ABCD
A
BC
D
with side
10
10
10
. On sides BC and
A
D
AD
A
D
of this square are selected respectively points
E
E
E
and
F
F
F
such that formed a rectangle
A
B
E
F
ABEF
A
BEF
. Rectangle
K
L
M
N
KLMN
K
L
MN
is located so that its the vertices
K
,
L
,
M
K, L, M
K
,
L
,
M
and
N
N
N
lie one on each segments
C
D
,
D
F
,
F
E
CD, DF, FE
C
D
,
D
F
,
FE
and
E
C
EC
EC
, respectively. It turned out that the rectangles
A
B
E
F
ABEF
A
BEF
and
K
L
M
N
KLMN
K
L
MN
are equal with
A
B
=
M
N
AB = MN
A
B
=
MN
. Find the length of segment
A
L
AL
A
L
.
geometry
rectangle
square