Question

In in triangle abc angle b is obtuse angle angle D is 90 degree prove that AC²=AB²+BC²+2AB.BD

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  ]