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
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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.
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