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Kvant 2021
M2662
M2662
Part of
Kvant 2021
Problems
(1)
Rays from vertices of parallelogram
Source: Kvant Magazine No. 8 2021 M2662
3/9/2023
In the parallelogram
A
B
C
D
ABCD
A
BC
D
, rays are released from its vertices towards its interior. The rays coming out of the vertices
A
A{}
A
and
D
D{}
D
intersect at
E
E{}
E
and the rays coming out of the vertices
B
B{}
B
and
C
C{}
C
at point
F
F{}
F
. It is known that
∠
B
A
E
=
∠
B
C
F
\angle BAE=\angle BCF
∠
B
A
E
=
∠
BCF
and
∠
C
D
E
=
∠
C
B
F
\angle CDE = \angle CBF
∠
C
D
E
=
∠
CBF
. Prove that
A
B
∥
E
F
AB \parallel EF
A
B
∥
EF
.Proposed by V. Eisenstadt
geometry
Kvant