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Answer :
By applying Pythagoras Theorem in \(\triangle\) ADB, we get,
\(AB^2 = AD^2 + DB^2\) ……………………… (i)
Again, by applying Pythagoras Theorem in \(\triangle\) ACD, we get,
\(AC^2 = AD^2 + DC^2\)
\(AC^2 = AD^2 + (DB + BC)^2\)
\(AC^2 = AD^2 + DB^2 + BC^2 + 2DB × BC\)
From equation (i), we can write,
\(AC^2 = AB^2 + BC^2 + 2DB × BC\)
Hence, proved.