Question

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

Answer 1

Construct $\to$ Drawn DY parallel to BX

To prove $\to \frac{BE}{EX}=3$

Proof :- In $\Delta ADY$ using midpoint theorem

$EX=\frac{DY}{2}$

also in $\Delta BCX$ using midpoint theorem

$DY=\frac{BX}{2}$

$\therefore EX=\frac{BX}{4}$

or, $4EX=BX$

$4EX=BE+EX$

$3EX=BE$

$\frac{BE}{EX}=3$

Proved