In a `/_\ABC `points D,E,F are taken on the sides BC,CA and AB respectively such that `(BD)/(DC)=(CE)/(EA)=(AF)/(FB)=n` prove that `/_\DEF= (n^2-n+1)/((n+1)^2)` `/_\ABC`

If D,E and F are three points on the sides BC,CA and AB, respectively,of a triangle ABC such that the (BD)/(CD),(CE)/(AE),(AF)/(BF)=-1

In a hat harr ABC,D and E are points on sides AB and AC respectively such that BD=CE. If /_B=/_C, show that DE|BC.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

If D and E are points on sides AB and AC respectively of a ABC such that DEBC and BD=CE. Prove that ABC is isosceles.

If D,E and F are the midpoints of sides BC,CA, and Ab respectively of /_ABC then using coordinate geometry prove that Area of /_DEF=(1)/(4) (Area of /_ABC)

In trigle ABC, the points D, E, F are the midpoints of the sides BC,CA, and AB respee. Tively. Using vector methed ,show that the area of Delta DEF is equal to (1)/(4) (area of ABC).