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2018 Stanford Mathematics Tournament
9
9
Part of
2018 Stanford Mathematics Tournament
Problems
(1)
SMT 2018 Geometry #9 cyclic quad
Source:
8/8/2023
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral with
3
A
B
=
2
A
D
3AB = 2AD
3
A
B
=
2
A
D
and
B
C
=
C
D
BC = CD
BC
=
C
D
. The diagonals
A
C
AC
A
C
and
B
D
BD
B
D
intersect at point
X
X
X
. Let
E
E
E
be a point on
A
D
AD
A
D
such that
D
E
=
A
B
DE = AB
D
E
=
A
B
and
Y
Y
Y
be the point of intersection of lines
A
C
AC
A
C
and
B
E
BE
BE
. If the area of triangle
A
B
Y
ABY
A
B
Y
is
5
5
5
, then what is the area of quadrilateral
D
E
Y
X
DEY X
D
E
Y
X
?
geometry