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Mathematics
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
,
D
D
D
is a point on
A
B
AB
A
B
such that
A
D
D
B
=
2
1
\frac{AD}{DB} = \frac{2}{1}
D
B
A
D
=
1
2
, and
E
E
E
is a point on
A
C
AC
A
C
such that
A
E
E
C
=
1
3
\frac{AE}{EC} = \frac{1}{3}
E
C
A
E
=
3
1
. The segments
C
D
CD
C
D
and
B
E
BE
B
E
intersect at
F
F
F
. Using Menelaus' Theorem or otherwise, determine the ratio
B
F
F
E
\frac{BF}{FE}
F
E
B
F
.
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