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Turkey Contests
Turkey Junior National Olympiad
2009 Turkey Junior National Olympiad
1
1
Part of
2009 Turkey Junior National Olympiad
Problems
(1)
Turkey Junior Olympiad 2009, Part II - P1
Source:
1/20/2013
Let the tangent line passing through a point
A
A
A
outside the circle with center
O
O
O
touches the circle at
B
B
B
and
C
C
C
. Let
[
B
D
]
[BD]
[
B
D
]
be the diameter of the circle. Let the lines
C
D
CD
C
D
and
A
B
AB
A
B
meet at
E
E
E
. If the lines
A
D
AD
A
D
and
O
E
OE
OE
meet at
F
F
F
, find
∣
A
F
∣
/
∣
F
D
∣
|AF|/|FD|
∣
A
F
∣/∣
F
D
∣
.