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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2005 Sharygin Geometry Olympiad
1
1
Part of
2005 Sharygin Geometry Olympiad
Problems
(1)
perpendicular non intersecting chords wanted
Source: Sharygin 2005 VIII CR 1
8/18/2019
The chords
A
C
AC
A
C
and
B
D
BD
B
D
of the circle intersect at point
P
P
P
. The perpendiculars to
A
C
AC
A
C
and
B
D
BD
B
D
at points
C
C
C
and
D
D
D
, respectively, intersect at point
Q
Q
Q
. Prove that the lines
A
B
AB
A
B
and
P
Q
PQ
PQ
are perpendicular.
geometry
Chords
perpendicular