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National and Regional Contests
Serbia Contests
Serbia Team Selection Test
1985 Yugoslav Team Selection Test
Problem 2
angles in parallelogram
angles in parallelogram
Source: Yugoslav TST 1985 P2
May 28, 2021
geometry
parallelogram
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram and let
E
E
E
be a point in the plane such that
A
E
⊥
A
B
AE\perp AB
A
E
⊥
A
B
and
B
C
⊥
E
C
BC\perp EC
BC
⊥
EC
. Show that either
∠
A
E
D
=
∠
B
E
C
\angle AED=\angle BEC
∠
A
E
D
=
∠
BEC
or
∠
A
E
D
+
∠
B
E
C
=
18
0
∘
\angle AED+\angle BEC=180^\circ
∠
A
E
D
+
∠
BEC
=
18
0
∘
.
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