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Area of quadrilateral ABCD - JBMO Shortlist
Area of quadrilateral ABCD - JBMO Shortlist
Source:
October 30, 2010
geometry
geometry proposed
Problem Statement
Consider a quadrilateral with
∠
D
A
B
=
6
0
∘
\angle DAB=60^{\circ}
∠
D
A
B
=
6
0
∘
,
∠
A
B
C
=
9
0
∘
\angle ABC=90^{\circ}
∠
A
BC
=
9
0
∘
and
∠
B
C
D
=
12
0
∘
\angle BCD=120^{\circ}
∠
BC
D
=
12
0
∘
. The diagonals
A
C
AC
A
C
and
B
D
BD
B
D
intersect at
M
M
M
. If
M
B
=
1
MB=1
MB
=
1
and
M
D
=
2
MD=2
M
D
=
2
, find the area of the quadrilateral
A
B
C
D
ABCD
A
BC
D
.
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