In triangle A B C ,points D , Ea n dF ar...

In triangle `A B C` ,points `D , Ea n dF` are taken on the sides `B C ,C Aa n dA B ,` respectively, such that `(B D)/(D C)=(C E)/(E A)=(A F)/(F B)=ndot` Prove that `triangle D E F=(n^2-n+1)/((n+1)^2) triangle(A B C)dot`

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