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1
SMT 2022 Geometry #1
SMT 2022 Geometry #1
Source:
April 1, 2023
Problem Statement
Points
A
A
A
,
B
B
B
,
C
C
C
, and
D
D
D
lie on a circle. Let
A
C
AC
A
C
and
B
D
BD
B
D
intersect at point
E
E
E
inside the circle. If
[
A
B
E
]
⋅
[
C
D
E
]
=
36
[ABE]\cdot[CDE]=36
[
A
BE
]
⋅
[
C
D
E
]
=
36
, what is the value of
[
A
D
E
]
⋅
[
B
C
E
]
[ADE]\cdot[BCE]
[
A
D
E
]
⋅
[
BCE
]
? (Given a triangle
△
A
B
C
\triangle ABC
△
A
BC
,
[
A
B
C
]
[ABC]
[
A
BC
]
denotes its area.)
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