Question

Abc is a right angled triangle right angled at b and p is the mid point of bc .Prove that ac^2=4ad^2-3ab^2

Answer 1

GIVEN:

ABC is a right angled at B and D is the midpoint of BC.

In ∆ABD

AD²= AB²+BD²…………(1)

[By Pythagoras theorem]

In ∆ ABC

AC²= AB²+BC²…………(2)

From equation (1)

AD²= AB²+ (BC/2)²

[D is the midpoint of BC]

AD²= AB²+ BC²/4

AD²= AB²/1+ BC²/4

4AD²= 4AB²+ BC²

BC²= 4AD²-4AB²…………….(3)

Using the value of BC² in eq. 2

AC²=AB²+4AD²-4AB²

AC²=AB²-4AB+4AD²

AC²= 4AD²-3AB²

HENCE PROVED….

HOPE THIS WILL