AD and BE are medians of `DeltaABC. F' lies on CE and BE"||"DF`. Prove that `CF=(1/4)AC.`

E is the mid-point of AD , a median of the Delta ABC . The extended BE intersects AC at F. prove that AF=(1)/(3)AC.

AD and BE are the medians of the triangle ABC. Prove that DeltaACD=DeltaBCE .

In the right-angled ABC, /_A =1 right angle. BE and CF are two medians of Delta ABC . Prove that 4 ( BE^(2) + CF^(2)) =5 BC^(2)

D, E and F are the mid-points of the sides AB, BC and CA of the DeltaABC . Prove that DeltaDEF=1/4DeltaABC .

(ix) AD, BE and CF are the three medians of Delta ABC and intersect at G. The area of the Delta ABC is 36 Sq. cm. Find (a) the area of Delta AGB and (b) the area of the quadrilateral BDGF.

D, E and F are the mid-points of the sides AB, AC and BC of the DeltaABC. Prove that DE and AF bisects each other.

AD is a diameter of the circumcircle of DeltaABC . AE is perpendicular to BC . Prove that ABxxAC=ADxxAE .

If E be the mid-point of the median AD of DeltaABC , then prove that DeltaBED=1/4DeltaABC .

The incircle of Delta ABC touches the sides AB, BC and CA of the triangle at the points D, E and F. Prove that AD + BE +CF=AF+CE +BD=1/2 (The perimeter of DeltaABC )