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3
2015 Geometry #3
2015 Geometry #3
Source:
December 23, 2016
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral with
∠
B
A
D
=
∠
A
B
C
=
9
0
∘
\angle BAD = \angle ABC = 90^{\circ}
∠
B
A
D
=
∠
A
BC
=
9
0
∘
, and suppose
A
B
=
B
C
=
1
AB=BC=1
A
B
=
BC
=
1
,
A
D
=
2
AD=2
A
D
=
2
. The circumcircle of
A
B
C
ABC
A
BC
meets
A
D
‾
\overline{AD}
A
D
and
B
D
‾
\overline{BD}
B
D
at point
E
E
E
and
F
F
F
, respectively. If lines
A
F
AF
A
F
and
C
D
CD
C
D
meet at
K
K
K
, compute
E
K
EK
E
K
.
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