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Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
1995 Mexico National Olympiad
5
5
Part of
1995 Mexico National Olympiad
Problems
(1)
5 triangles with equal areas in a convex pentagon
Source: Mexican Mathematical Olympiad 1995 OMM P5
7/28/2018
A
B
C
D
E
ABCDE
A
BC
D
E
is a convex pentagon such that the triangles
A
B
C
,
B
C
D
,
C
D
E
,
D
E
A
ABC, BCD, CDE, DEA
A
BC
,
BC
D
,
C
D
E
,
D
E
A
and
E
A
B
EAB
E
A
B
have equal areas. Show that
(
1
/
4
)
(1/4)
(
1/4
)
area
(
A
B
C
D
E
)
<
(ABCDE) <
(
A
BC
D
E
)
<
area
(
A
B
C
)
<
(
1
/
3
)
(ABC) < (1/3)
(
A
BC
)
<
(
1/3
)
area
(
A
B
C
D
E
)
(ABCDE)
(
A
BC
D
E
)
.
geometry
pentagon
areas