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Problems
Contests
National and Regional Contests
South Africa Contests
South Africa National Olympiad
2003 South africa National Olympiad
4
4
Part of
2003 South africa National Olympiad
Problems
(1)
Pentagon and triangles with equal areas
Source: South Africa 2003
10/14/2005
In a given pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
, triangles
A
B
C
ABC
A
BC
,
B
C
D
BCD
BC
D
,
C
D
E
CDE
C
D
E
,
D
E
A
DEA
D
E
A
and
E
A
B
EAB
E
A
B
all have the same area. The lines
A
C
AC
A
C
and
A
D
AD
A
D
intersect
B
E
BE
BE
at points
M
M
M
and
N
N
N
. Prove that
B
M
=
E
N
BM = EN
BM
=
EN
.
geometry
geometry proposed