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Portugal Contests
Portugal MO
2014 Portugal MO
5
5
Part of
2014 Portugal MO
Problems
(1)
FINALS - Portuguese Mathematical Olympiad (High-School) P5
Source:
4/6/2014
Let
[
A
B
C
D
]
[ABCD]
[
A
BC
D
]
be a convex quadrilateral with area
2014
2014
2014
, and let
P
P
P
be a point on
[
A
B
]
[AB]
[
A
B
]
and
Q
Q
Q
a point on
[
A
D
]
[AD]
[
A
D
]
such that triangles
[
A
B
Q
]
[ABQ]
[
A
BQ
]
and
[
A
D
P
]
[ADP]
[
A
D
P
]
have area
1
1
1
. Let
R
R
R
be the intersection of
[
A
C
]
[AC]
[
A
C
]
and
[
P
Q
]
[PQ]
[
PQ
]
. Determine
R
C
‾
R
A
‾
\frac{\overline{RC}}{\overline{RA}}
R
A
RC
.
geometry
geometry unsolved