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Honduran Mathematical Olympiad
2021 Honduras National Mathematical Olympiad
Problem 4
Problem 4
Part of
2021 Honduras National Mathematical Olympiad
Problems
(1)
Honduran National MO (OHM) Intermediate Problem 4
Source: 2021 OHM Intermediate P4
11/21/2021
Consider parallelogram
A
B
C
D
ABCD
A
BC
D
and let
E
E
E
be the midpoint of
B
C
BC
BC
. In segment
D
E
DE
D
E
a point
F
F
F
is chosen such that
A
F
AF
A
F
is perpendicular to
D
E
DE
D
E
. Prove that
∠
C
D
E
=
∠
E
F
B
\angle CDE=\angle EFB
∠
C
D
E
=
∠
EFB
.
geometry