If `D , E ,a n dF` are three points on the sides `B C ,A C ,a n dA B` of a triangle `A B C` such that `A D ,B E ,a n dC F` are concurrent, then show that `BD*CE*AF=DC*EA*FB` .

If D,E, and F are three points on the sides BC,AC, and AB of a triangle ABC such that AD,BE, and CF are concurrent,then show that BD*CE*AF=DC*EA*FB

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that AD,BE and CF are concurrent, then show that (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that the (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

If D ,E and F are three points on the sides B C ,CA and A B , respectively, of a triangle A B C show that the (B D)/(C D)=(C E)/(A E)=(A F)/(B F)=-1

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot