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Contests
International Contests
Baltic Way
2005 Baltic Way
12
12
Part of
2005 Baltic Way
Problems
(1)
AD and BC meet MN at P and Q
Source: Baltic Way 2005
12/28/2010
Let
A
B
C
D
ABCD
A
BC
D
be a convex quadrilateral such that
B
C
=
A
D
BC=AD
BC
=
A
D
. Let
M
M
M
and
N
N
N
be the midpoints of
A
B
AB
A
B
and
C
D
CD
C
D
, respectively. The lines
A
D
AD
A
D
and
B
C
BC
BC
meet the line
M
N
MN
MN
at
P
P
P
and
Q
Q
Q
, respectively. Prove that
C
Q
=
D
P
CQ=DP
CQ
=
D
P
.
geometry
parallelogram
rhombus
trigonometry
geometry proposed