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Sharygin Geometry Olympiad
2012 Sharygin Geometry Olympiad
14
14
Part of
2012 Sharygin Geometry Olympiad
Problems
(1)
Ratio of triangle areas
Source: Sharygin Geometry Olympiad 2012 - Problem 14
4/28/2012
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
suppose
A
C
∩
B
D
=
O
AC \cap BD = O
A
C
∩
B
D
=
O
and
M
M
M
is the midpoint of
B
C
BC
BC
. Let
M
O
∩
A
D
=
E
MO \cap AD = E
MO
∩
A
D
=
E
. Prove that
A
E
E
D
=
S
△
A
B
O
S
△
C
D
O
\frac{AE}{ED} = \frac{S_{\triangle ABO}}{S_{\triangle CDO}}
E
D
A
E
=
S
△
C
D
O
S
△
A
BO
.
ratio
geometry
geometry unsolved