Question

Prove that AC2 =AD2+BC×ED+BC2/4

Answer 1

Given that in a ΔABC in which ∠B is obtuse and AD ⊥ BC.

To prove: AC2 = AB2 + BC2 + 2 BC X BD

Proof:

In ΔADC,

AC2 = AD2 + DC2 ( Pythagoras theorem)

AC2 = AD2 + (DB + BC)2

AC2 = AD2 + DB2 + BC2 + 2DB X BC.

AC2 = AB2 + BC2 + 2 DB X BC. [ ∴ AD2 + DB2 = AB2 ]

if you do in this way