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Soros Olympiad in Mathematics
VII Soros Olympiad 2000 - 01
9.7
9.7
Part of
VII Soros Olympiad 2000 - 01
Problems
(1)
area chasing, 2 equal ratios in quadrilateral (VII Soros Olympiad R1 9.7)
Source:
7/4/2021
Sides
A
B
AB
A
B
and
C
D
CD
C
D
of quadrilateral
A
B
C
D
ABCD
A
BC
D
intersect at point
E
E
E
. On the diagonals
A
C
AC
A
C
and
B
D
BD
B
D
points
M
M
M
and
N
N
N
are taken, respectively, so that
A
M
/
A
C
=
B
N
/
B
D
=
k
AM / AC = BN / BD = k
A
M
/
A
C
=
BN
/
B
D
=
k
. Find the area of a triangle
E
M
N
EMN
EMN
if the area of
A
B
C
D
ABCD
A
BC
D
is
S
S
S
.
geometry
areas