Let ABC be a triangle, right-angled at C. If D is the mid-point of BC, prove that AB² = 4AD² – 3AC².
                                             

Given: ABC be a triangle, right-angled at C and D is the mid-point of BC.
To Prove: AB² = 4AD² – 3AC².
Proof:
From right triangle ACB, we have,
AB² = AC² + BC²
     = AC² + (2CD)² = AC² + 4CD²       [Since BC = 2CD]
     = AC² + 4(AD² - AC²)                  [From right Δ ACD]
 
     = 4AD² – 3AC².