E is the mid-point of the median AD of `DeltaABC.` Line segment BE meets AC at point F when produce, prove that `AF=1/3AC.`

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that : BP=2AD

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that: PB=2AD

In a triangle ABC, AD is a median and E is mid-point of median AD. A line through B and E meets AC at point E. Prove that : AC = 3AF Draw DG parallel to BF, which meets AC at point G.

The median AD of the triangle ABC is bisected at E and BE meets AC at F. Find AF:FC.

The median AD of the triangle ABC is bisected at E and BE meets AC at F. Find AF:FC.

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that: O is mid-point of AP.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Prove that BDFE is a parallelogram

In A ABC, E is mid-point of the median AD and BE produced meets side AC at point Q. Show that BE : EQ = 3:1.

In figure, P is the mid-point of B C , ,Q is the mid-point of A P , such that B Q produced meets A C at Rdot Prove that 3RA= CA

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