Question

In the figure ABC is a right angled trian
gles at C and D is the midpoint BC prove that ABsquare =4 AD square -3ACsquare

Answer 1

Step-by-step explanation:

Given: CD = BC/2

            ∠C = 90°

To Prove: AB²= 4AD² - 3AC²

Proof:

AD²=CD²+AC²

CD= BC/2                   [GIVEN]

⇒AD²= [BC/2]² + AC²

⇒AD²= BC²/4 + AC²

⇒AD²= [BC²+4AC²] / 4

⇒4AD²=BC²+4AC²

But, BC²=AB² - AC²

Substituting value of BC²,

⇒AB²- AC² + 4AC² = 4AD²

⇒AB²+3AC²=4AD²

⇒AB²=4AD²-3AC²

Thus Proved.