Question

In right angled triangle ABCIn which angle c=90,if D is the mid point of BC,prove that AB^2=4AD^2-3AC^2

Answer 1

Answer:

Step-by-step explanation:

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 HELP YOU…

Read more on Brainly.in - https://brainly.in/question/2090096#readmore