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Moldova National Olympiad
2009 Moldova National Olympiad
8.3
8.3
Part of
2009 Moldova National Olympiad
Problems
(1)
\\ wanted, intersecting circles, tangents (2009 Moldova NMO 8.3)
Source:
3/25/2021
The circle
C
1
C_1
C
1
of center
O
O
O
and the circle
C
2
C_2
C
2
intersect at points
A
A
A
and
B
B
B
, so that point
O
O
O
lies on circle
C
2
C_2
C
2
. The lines
d
d
d
and
e
e
e
are tangent at point
A
A
A
to the circles
C
1
C_1
C
1
and
C
2
C_2
C
2
respectively. If the line
e
e
e
intersects the circle
C
1
C_1
C
1
at point
D
D
D
, prove that the lines
B
D
BD
B
D
and
d
d
d
are parallel.
parallel
geometry
circles