Question

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

Answer 1

Explanation:

Given that ABC is a triangle.

D is the midpoint of side BC.

Also, given that AD is bisected at the point E and BE produced cuts AC at the point X.

To prove that : $\ {BE}: \ {EX}=3: 1$

Let us draw $DF \| BX$

Let us consider the triangle ADY,

Using the midpoint theorem, we have,

 $E X=\frac{D Y}{2}$

$2EX=DY$ ------------(1)

Now, let us consider the triangle BCX,

Using the midpoint theorem, we have,

$D Y=\frac{B X}{2}$

Substituting $2EX=DY$, we get,

$2EX=\frac{B X}{2}$

$4E X=BX$

Since, $B X=B E+E X$ , we get,

$4 E X=B E+E X$

$3 E X=B E$

  $\frac{B E}{E X}=\frac{3}{1}$

Thus, $\ {BE}: \ {EX}=3: 1$

Hence proved

Learn more:

(1) 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

brainly.in/question/6104080

(2) D is the mid point of side BC of a triangle ABC. AD is bisected at the point E and be produced cuts AC at X . Prove that BE:EX=3:1.​

brainly.in/question/11194445