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Problems
Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
1999 Flanders Math Olympiad
2
2
Part of
1999 Flanders Math Olympiad
Problems
(1)
circle chord
Source: flanders '99/2
9/27/2005
Let
[
m
n
]
[mn]
[
mn
]
be a diameter of the circle
C
C
C
and
[
A
B
]
[AB]
[
A
B
]
a chord with given length on this circle.
[
A
B
]
[AB]
[
A
B
]
neither coincides nor is perpendicular to
[
M
N
]
[MN]
[
MN
]
. Let
C
,
D
C,D
C
,
D
be the orthogonal projections of
A
A
A
and
B
B
B
on
[
M
N
]
[MN]
[
MN
]
and
P
P
P
the midpoint of
[
A
B
]
[AB]
[
A
B
]
. Prove that
∠
C
P
D
\angle CPD
∠
CP
D
does not depend on the chord
[
A
B
]
[AB]
[
A
B
]
.