D is the midpoint of side BC of a triangle ABC.AD is bisected at a point E and BE produced cuts AC at the point X.Prove that - BE : EX = 3:1

Given:∆ABC where D is the mid point of BC, E is the mid point AD. BE produced meets AC at X.

To Prove:BE : EX = 3:1

Proof:

Comparing ∆BCX and ∆DCY:

BCX = DCY(Common)

BXC = DYC(Corresponding angles)

So,∆BCX ∼ ∆DCY(AA Similarity test)