Question

in triangle ABC if BD is perpendicular AC and BC square =2AC×CD prove AB=AC

Answer 1

hope it helps you......

Answer 2

Answer:

The proof is given below.

Step-by-step explanation:

Given in triangle ABC if BD is perpendicular AC and $BC^2=2(AC)(CD)$ then we have to prove that AB=AC.

By Pythagoras theorem

$BC^2=BD^2+DC^2$  →    (1)

$AB^2=BD^2+AD^2$  →    (2)

Now, given

$BC^2=2(AC)(CD)$

⇒ $BD^2+CD^2=2(AC)(CD)$      (∵ Using 1)

⇒ $(AB^2-AD^2)+CD^2=2(AC)(CD)$    (∵ Using 2)

⇒ $AB^2-(AC-CD)^2+CD^2=2(AC)(CD)$

⇒ $AB^2-AC^2-CD^2+2(AC)(CD)+CD^2=2(AC)(CD)$

⇒ $AB^2=AC^2$

⇒ $AB=AC$

Hence Proved.