MathDB
Problems
Contests
International Contests
Caucasus Mathematical Olympiad
2022 Caucasus Mathematical Olympiad
2
2
Part of
2022 Caucasus Mathematical Olympiad
Problems
(1)
Easy similarity in parallelogram
Source: VII Caucasus Mathematical Olympiad
3/13/2022
In parallelogram
A
B
C
D
ABCD
A
BC
D
, points
E
E
E
and
F
F
F
on segments
A
D
AD
A
D
and
C
D
CD
C
D
are such that
∠
B
C
E
=
∠
B
A
F
\angle BCE=\angle BAF
∠
BCE
=
∠
B
A
F
. Points
K
K
K
and
L
L
L
on segments
A
D
AD
A
D
and
C
D
CD
C
D
are such that
A
K
=
E
D
AK=ED
A
K
=
E
D
and
C
L
=
F
D
CL=FD
C
L
=
F
D
. Prove that
∠
B
K
D
=
∠
B
L
D
\angle BKD=\angle BLD
∠
B
KD
=
∠
B
L
D
.
geometry
parallelogram
number theory