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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2021 Sharygin Geometry Olympiad
9
9
Part of
2021 Sharygin Geometry Olympiad
Problems
(1)
Equal angles in a parallelogram
Source: XVII Sharygin Correspondence Round P9
3/2/2021
Points
E
E
E
and
F
F
F
lying on sides
B
C
BC
BC
and
A
D
AD
A
D
respectively of a parallelogram
A
B
C
D
ABCD
A
BC
D
are such that
E
F
=
E
D
=
D
C
EF=ED=DC
EF
=
E
D
=
D
C
. Let
M
M
M
be the midpoint of
B
E
BE
BE
and
M
D
MD
M
D
meet
E
F
EF
EF
at
G
G
G
. Prove that
∠
E
A
C
=
∠
G
B
D
\angle EAC=\angle GBD
∠
E
A
C
=
∠
GB
D
.
geometry
parallelogram