In , points and are taken on the sides and , respectively such that BD DC = CE EA =…

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

In △ABC\triangle ABC , points D,ED, E and FF are taken on the sides BC,CABC, CA and ABAB , respectively such that BDDC=CEEA=AFFB=n.\frac{BD}{DC} = \frac{CE}{EA} = \frac{AF}{FB} = n. Prove that, △DEF=n2−n+1(n+1)2△ABC.\text{Prove that, } \triangle DEF = \frac{n^2 - n + 1}{(n+1)^2} \triangle ABC.

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