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Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
2003 Mexico National Olympiad
4
4
Part of
2003 Mexico National Olympiad
Problems
(1)
simple geometry
Source: Mexico 2003
3/2/2007
The quadrilateral
A
B
C
D
ABCD
A
BC
D
has
A
B
AB
A
B
parallel to
C
D
CD
C
D
.
P
P
P
is on the side
A
B
AB
A
B
and
Q
Q
Q
on the side
C
D
CD
C
D
such that
A
P
P
B
=
D
Q
C
Q
\frac{AP}{PB}= \frac{DQ}{CQ}
PB
A
P
=
CQ
D
Q
. M is the intersection of
A
Q
AQ
A
Q
and
D
P
DP
D
P
, and
N
N
N
is the intersection of
P
C
PC
PC
and
Q
B
QB
QB
. Find
M
N
MN
MN
in terms of
A
B
AB
A
B
and
C
D
CD
C
D
.
geometry