Question

AD is the altitude from A in the ΔABC and DB : CD = 3 : 1. Prove that BC² = 2 (AB² − AC²).

Answer 1

In ΔABC, AD ⊥ BC and DB : CD = 3: 1.

Applying Pythagoras theorem in ΔABD and ΔADC, we have:

… (1)

… (2)

From equations (1) and (2), we have: