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`

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

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.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD is perpendicular to EF.

O is any point in the plane of the triangle ABC,AO,BO and CO meet the sides BC,CA nd AB in D,E,F respectively show that (OD)/(AD)+(OE)/(BE)+(OF)/(CF)=1.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD and FE bisect each other.

If D , E and F are the mid-points of the sides BC , CA and AB respectively of the DeltaABC and O be any point, then prove that OA+OB+OC=OD+OE+OF

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that A E^2+B D^2=A B^2+D E^2 .

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that A E^2+B D^2=A B^2+D E^2 .

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

If D ,Ea n dF are the mid-points of sides BC, CA and AB respectively of a A B C , then using coordinate geometry prove that Area of △DEF= 1/4 (Area of △ABC)