Question

In right-angled triangle ABC in which ∠C=90⁰, if D is the mid-point of BC, prove that AB²=4AD²-3AC².

Answer 1

Here is your answer

Attachments:

Answer 2

AB² = 4AD² - 3AC² proved

Step-by-step explanation:

Given: ΔABC is right - angled at C. D is the mid-point of BC.

To Prove: AB² = 4AD² - 3AC².

Proof:

In  ΔABC, we know that:

AB² = AC² + BC²

= AC² + (2CD)²

= AC² + 4CD² [as BC = 2CD]

= AC² + 4(AD² - AC²) [From ΔACD right angled at C]

AB² = 4AD² - 3AC².  

Hence proved. Please find attached diagram.