Question

D is the mid point of side BC of triangle ABC and E of AD. BE produced meets AC at the point M. Prove that BE=3ME.
Plzzz help I have my exam tomorrow.

Answer 1

​
Let's take point Y on seg AC such that DY | | BX.

As D is a midpoint of BC, by converse of midpoint theorem, XY=YC.

Applying midpoint theorem in triangle CDY,BX=2DY.

As E is a midpoint of AD & EX | | DY, 
AX=XY.

Applying midpoint theorem in triangle DAY,EX= DY/2

BE/EX = BX-EX / EX 
            = 2DY - DY/2 / DY/2
             = 3DY / 2 * 2/YD
               = 3DY/DY
                = 3:1.

Hope its help you