In `Delta ABC`, AD is a median and E is the midpoint of AD. BE is extended to intersect AC at F. Prove that `AF = (1)/(3)AC`.

In triangleABC , AD is a median . E is the midpoint of AD and F is the midpoint of AE. Prove that ar(ABF)= 1/8 ar(ABC).

In trapezium ABCD, AB || CD and E is the midpoint of AD. A line drawn through E and parallel to AB intersects BC at F. Prove that F is the midpoint of BC and EF = (1)/(2)(AB + CD) .

In triangle ABC, AD is a median. Prove that AB + AC gt 2AD

In a triangle ABC, AD is the median drawn on the side BC is produced to E such that AD = ED prove that ABEC is a parallelogram.

In Delta ABC , point M on AB and point N on AC are such that AM = (1)/(4)AC and AN =(1)/(4)AC . Prove that MN =(1)/(4) BC

ABC is a triangle with AB= AC and D is a point on AC such that BC^(2)= AC xx CD . Prove that BD= BC.

In triangle ABC,D is the midpoint of AB, E is the midpoint of DB and F is the midpoint of BC. If the area of DeltaABC is 96, the area of DeltaAEF is

In DeltaABC , E and F are the midpoints of AB and AC respectively. If EF = 4 cm, then BC= ……….. Cm

In the given figure, AB is a diameter of the circle, CD is chord equal to the radius of the circle, AC and BD when extended intersect at a point E. Prove that angle AEB = 60^(@).

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