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06/06/2021 12:46 pm
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In Figure, ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that
AC2= AB2+ BC2+ 2BC.BD.
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06/06/2021 12:47 pm
By applying Pythagoras Theorem in ∆ADB, we get,
AB2 = AD2 + DB2 ……………………… (i)
Again, by applying Pythagoras Theorem in ∆ACD, we get,
AC2 = AD2 + DC2
AC2 = AD2 + (DB + BC) 2
AC2 = AD2 + DB2 + BC2 + 2DB × BC
From equation (i), we can write,
AC2 = AB2 + BC2 + 2DB × BC
Hence, proved.