MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Junior National Olympiad
1999 Turkey Junior National Olympiad
1
Turkey Junior Olympiad 1999, Part II - P1
Turkey Junior Olympiad 1999, Part II - P1
Source:
January 18, 2013
Problem Statement
The chord
[
C
D
]
[CD]
[
C
D
]
is parallel to the diameter
[
A
B
]
[AB]
[
A
B
]
of a circle with center
O
O
O
. The tangent line at
A
A
A
meet
B
C
BC
BC
and
B
D
BD
B
D
at
E
E
E
and
F
F
F
. If
∣
A
B
∣
=
10
|AB|=10
∣
A
B
∣
=
10
, calculate
∣
A
E
∣
⋅
∣
A
F
∣
|AE|\cdot |AF|
∣
A
E
∣
⋅
∣
A
F
∣
.
Back to Problems
View on AoPS