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International Contests
Cono Sur Olympiad
Cono Sur Shortlist - geometry
1993.2
1993.2
Part of
Cono Sur Shortlist - geometry
Problems
(1)
trapezoid and areas wanted - 1993 Cono Sur Shortlist G2
Source:
10/23/2021
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral and let
O
O
O
be the point of intersection of diagonals
A
C
AC
A
C
and
B
D
BD
B
D
. Knowing that the area of triangle
A
O
B
AOB
A
OB
is equal to
1
1
1
, the area of triangle
B
O
C
BOC
BOC
is equal to
2
2
2
, and the area of triangle
C
O
D
COD
CO
D
is equal to
4
4
4
, calculate the area of triangle
A
O
D
AOD
A
O
D
and prove that
A
B
C
D
ABCD
A
BC
D
is a trapezoid.
geometry
trapezoid