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2022 CMIMC
1.8
2022 Geo Div 1 P8
2022 Geo Div 1 P8
Source:
February 28, 2022
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral with circumcenter
O
O
O
. Rays
O
B
→
\displaystyle \overrightarrow{OB}
OB
and
D
C
→
\displaystyle \overrightarrow{DC}
D
C
intersect at
E
E
E
, and rays
O
C
→
\displaystyle \overrightarrow{OC}
OC
and
A
B
→
\displaystyle \overrightarrow{AB}
A
B
intersect at
F
F
F
. Suppose that
A
E
=
E
C
=
C
F
=
4
AE = EC = CF = 4
A
E
=
EC
=
CF
=
4
, and the circumcircle of
O
D
E
ODE
O
D
E
bisects
B
F
‾
\overline{BF}
BF
. Find the area of triangle
A
D
F
ADF
A
D
F
.Proposed by Howard Halim
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