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7
2004 HMMT Geometry # 7
2004 HMMT Geometry # 7
Source:
March 3, 2024
geometry
Problem Statement
Yet another trapezoid
A
B
C
D
ABCD
A
BC
D
has
A
D
AD
A
D
parallel to
B
C
BC
BC
.
A
C
AC
A
C
and
B
D
BD
B
D
intersect at
P
P
P
. If
[
A
D
P
]
=
[
B
C
P
]
=
1
/
2
[ADP]=[BCP] = 1/2
[
A
D
P
]
=
[
BCP
]
=
1/2
, find
[
A
D
P
]
/
[
A
B
C
D
]
[ADP]/[ABCD]
[
A
D
P
]
/
[
A
BC
D
]
. (Here the notation
[
P
1
.
.
.
P
n
]
[P_1 ...P_n]
[
P
1
...
P
n
]
denotes the area of the polygon
P
1
.
.
.
P
n
P_1 ...P_n
P
1
...
P
n
.)
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