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National and Regional Contests
Austria Contests
Austrian MO Beginners' Competition
2002 Austria Beginners' Competition
4
4
Part of
2002 Austria Beginners' Competition
Problems
(1)
construction of trapezoid and area wanted, <120^o
Source: 2002 Austria Beginners' Competition p4
10/4/2022
In a trapezoid
A
B
C
D
ABCD
A
BC
D
with base
A
B
AB
A
B
let
E
E
E
be the midpoint of side
A
D
AD
A
D
. Suppose further that
2
C
D
=
E
C
=
B
C
=
b
2CD=EC=BC=b
2
C
D
=
EC
=
BC
=
b
. Let
∠
E
C
B
=
12
0
∘
\angle ECB=120^{\circ}
∠
ECB
=
12
0
∘
. Construct the trapezoid and determine its area based on
b
b
b
.
geometry
trapezoid
construction