Question

In a right ΔABC right-angled at C, if D is the mid-point of BC, prove that BC²=4(AD²-AC²).

Answer 1

Answer:

Can be solved using Similar Triangle Proportion

Answer 2

AB² = 4(AD² - AC²) proved

Step-by-step explanation:

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

To Prove: AB² = 4(AD² - AC²).

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]

Hence proved. Please find attached diagram.