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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2005 Sharygin Geometry Olympiad
10.3
10.3
Part of
2005 Sharygin Geometry Olympiad
Problems
(1)
midpoint of a radius is equidistant from parallel chords of another circle
Source: Sharygin 2005 finals 10.3
8/29/2019
Two parallel chords
A
B
AB
A
B
and
C
D
CD
C
D
are drawn in a circle with center
O
O
O
. Circles with diameters
A
B
AB
A
B
and
C
D
CD
C
D
intersect at point
P
P
P
. Prove that the midpoint of the segment
O
P
OP
OP
is equidistant from lines
A
B
AB
A
B
and
C
D
CD
C
D
.
circles
Chords
parallel
distance
geometry