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Mathematics
Mathematics
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
, points
D
,
E
D, E
D
,
E
and
F
F
F
are taken on the sides
B
C
,
C
A
BC, CA
B
C
,
C
A
and
A
B
AB
A
B
, respectively such that
B
D
D
C
=
C
E
E
A
=
A
F
F
B
=
n
.
\frac{BD}{DC} = \frac{CE}{EA} = \frac{AF}{FB} = n.
D
C
B
D
=
E
A
C
E
=
F
B
A
F
=
n
.
Prove that,
△
D
E
F
=
n
2
−
n
+
1
(
n
+
1
)
2
△
A
B
C
.
\text{Prove that, } \triangle DEF = \frac{n^2 - n + 1}{(n+1)^2} \triangle ABC.
Prove that,
△
D
E
F
=
(
n
+
1
)
2
n
2
−
n
+
1
△
A
B
C
.
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