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Spain Mathematical Olympiad
2007 Spain Mathematical Olympiad
Problem 6
Problem 6
Part of
2007 Spain Mathematical Olympiad
Problems
(1)
Spain Mathematical Olympiad 2007, Problem 6
Source: 2007 Spain Mathematical Olympiad
6/15/2017
Given a halfcircle of diameter
A
B
=
2
R
AB = 2R
A
B
=
2
R
, consider a chord
C
D
CD
C
D
of length
c
c
c
. Let
E
E
E
be the intersection of
A
C
AC
A
C
with
B
D
BD
B
D
and
F
F
F
the inersection of
A
D
AD
A
D
with
B
C
BC
BC
. Prove that the segment
E
F
EF
EF
has a constant length and direction when varying the chord
C
D
CD
C
D
about the halfcircle.
geometry
circles