Question

in a triangle ABC, D is the mid point of Side BC. If a line is drawn from B in such a way that bisects AD and cut AD and AC at E and X respectively, then prove that EX/BE=1/3

Answer 1

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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.

Answer 2

Hope this will help u