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Austrian-Polish
2002 Austrian-Polish Competition
1
1
Part of
2002 Austrian-Polish Competition
Problems
(1)
Austrian-Polish Mathematical Olympiad 1992
Source:
4/28/2011
Given a circle
G
G
G
with center
O
O
O
and radius
r
r
r
. Let
A
B
AB
A
B
be a fixed diameter of
G
G
G
. Let
K
K
K
be a fixed point of segment
A
O
AO
A
O
. Denote by
t
t
t
the line tangent to at
A
A
A
. For any chord
C
D
CD
C
D
(other than
A
B
AB
A
B
) passing through
K
K
K
. Let
P
P
P
and
Q
Q
Q
be the points of intersection of lines
B
C
BC
BC
and
B
D
BD
B
D
with
t
t
t
. Prove that the product
A
P
ā
A
Q
AP\cdot AQ
A
P
ā
A
Q
remains costant as the chord
C
D
CD
C
D
varies.
ratio
geometry