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All-Russian Olympiad Regional Round
2004 All-Russian Olympiad Regional Round
8.6
8.6
Part of
2004 All-Russian Olympiad Regional Round
Problems
(1)
#, 2 midpoints, 2 circumenters - All-Russian MO 2004 Regional (R4) 8.6
Source:
9/27/2024
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral with parallel sides
A
D
AD
A
D
and
B
C
BC
BC
,
M
M
M
and
N
N
N
are the midpoints of its sides
A
B
AB
A
B
and
C
D
CD
C
D
, respectively. The straight line
M
N
MN
MN
bisects the segment connecting the centers of the circumcircles of triangles
A
B
C
ABC
A
BC
and
A
D
C
ADC
A
D
C
. Prove that
A
B
C
D
ABCD
A
BC
D
is a parallelogram.
geometry
parallelogram