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Answer :
By applying Pythagoras Theorem in \(\triangle\) ADB, we get,
\(AB^2 = AD^2 + DB^2\)
We can write it as;
\( AD^2 = AB^2 - DB^2 \)……………….. (i)
By applying Pythagoras Theorem in \(\triangle\) ADC, we get,
\(AD^2 + DC^2 = AC^2\)
From equation (i),
\(AB^2 - BD^2 + DC^2 = AC^2\)
\(AB^2 - BD^2 + (BC - BD)^2 = AC^2\)
\(AC^2 = AB^2 - BD^2 + BC^2 + BD^2 - 2BC × BD\)
\(AC^2= AB^2 + BC^2 - 2BC × BD\)
Hence, proved.