`D , E ,a n dF` are the middle points of the sides of the triangle `A B C` , then (a) centroid of the triangle `D E F` is the same as that of `A B C` (b) orthocenter of the tirangle`D E F` is the circumcentre of `A B C`

If D ,\ E and F are the mid-points of the sides of a /_\A B C , the ratio of the areas of the triangles D E F and ABC is .......

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 .

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a Delta A B C . Determine the ratio of the areas of D E F and A B C .

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 side B C ,\ C A and A B respectively of a triangle ABC, write the value of vec A D+ vec B E+ vec C Fdot

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

D , E , F are the foot of the perpendicular from vertices A , B , C to sides B C ,\ C A ,\ A B respectively, and H is the orthocentre of acute angled triangle A B C ; where a , b , c are the sides of triangle A B C , then H is the incentre of triangle D E F A , B ,\ C are excentres of triangle D E F Perimeter of D E F is a cos A+b cos B+c\ cos C Circumradius of triangle D E F is R/2, where R is circumradius of A B C

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 .

D is the mid-point of side B C of triangle A B C and E is the mid-point of B D . If O is the mid-point of A E , prove that a r(triangle B O E)=1/8a r(triangle A B C) .