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Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2013 Bangladesh Mathematical Olympiad
3
3
Part of
2013 Bangladesh Mathematical Olympiad
Problems
(1)
Find the area $0$
Source: Bangladesh National MO 2013
3/5/2019
Higher Secondary P3Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a regular hexagon with
A
B
=
7
AB=7
A
B
=
7
.
M
M
M
is the midpoint of
D
E
DE
D
E
.
A
C
AC
A
C
and
B
F
BF
BF
intersect at
P
P
P
,
A
C
AC
A
C
and
B
M
BM
BM
intersect at
Q
Q
Q
,
A
M
AM
A
M
and
B
F
BF
BF
intersect at
R
R
R
. Find the value of
[
A
P
B
]
+
[
B
Q
C
]
+
[
A
R
F
]
ā
[
P
Q
M
R
]
[APB]+[BQC]+[ARF]-[PQMR]
[
A
PB
]
+
[
BQC
]
+
[
A
RF
]
ā
[
PQMR
]
. Here
[
X
]
[X]
[
X
]
denotes the area of polygon
X
X
X
.
geometry