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2020 Latvia TST
1.1
1.1
Part of
2020 Latvia TST
Problems
(1)
Parallelograms
Source: 2020 Latvia TST Round 1
3/30/2020
It is given parallelogram
A
B
C
D
ABCD
A
BC
D
. On it's sides
A
B
,
B
C
,
C
D
,
D
A
AB, BC, CD, DA
A
B
,
BC
,
C
D
,
D
A
are chosen points
E
,
F
,
G
,
H
E, F, G, H
E
,
F
,
G
,
H
such that area of
E
F
G
H
EFGH
EFG
H
is half of the area of
A
B
C
D
ABCD
A
BC
D
. Show that at least one of the quadrilaterals
A
B
F
H
ABFH
A
BF
H
and
A
E
G
D
AEGD
A
EG
D
is parallelogram.
geometry
parallelogram