In the figure, ▲ ABC is an obtuse triangle, obtuse-angled at B. If \(AD \bot BC\), then

\(A{C^2} = A{D^2} + D{C^2}\)

\(\Rightarrow {AC^2} = A{D^2} + {[DB + BC]^2}\)

\(\Rightarrow {AC^2} = A{D^2} + D{B^2} + B{C^2} + 2BC \times BD\)

\(\Rightarrow A{C^2} = [A{D^2} + D{B^2}] + B{C^2} + 2BC \times BD\)

\(\Rightarrow A{C^2} = A{B^2} + B{C^2} + 2BC \times BD\)