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Akdeniz University MO
1999 Akdeniz University MO
5
geometry
geometry
Source:
January 31, 2016
geometry
Problem Statement
Let
C
C
C
is at a circle.
[
A
B
]
[AB]
[
A
B
]
is a diameter this circle.
D
D
D
is a point at
[
A
B
]
[AB]
[
A
B
]
. Perpendicular from
C
C
C
to
[
A
B
]
[AB]
[
A
B
]
's foot on the
[
A
B
]
[AB]
[
A
B
]
is
E
E
E
, perpendicular from
A
A
A
to
[
C
D
]
[CD]
[
C
D
]
's foot on the
[
C
D
]
[CD]
[
C
D
]
is
F
F
F
. Prove that,
[
D
C
]
[
F
C
]
=
[
B
D
]
[
E
A
]
[DC][FC]=[BD][EA]
[
D
C
]
[
FC
]
=
[
B
D
]
[
E
A
]
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