Q. 324.3( 33 Votes )

Δ ABC is ri

Answer :


Given: A ΔABC right-angled at B, and D is the mid-point of BC, i.e. BD = CD


To Prove: AC2 = (4AD2 - 3AB2)


Proof:


In ΔABD,


By Pythagoras theorem, [i.e. Hypotenuse2 = Base2+ Perpendicular2]


AD2 = AB2 + BD2


[ as D is mid-point of BC, therefore,



4AD2 = 4AB2 + BC2


BC2 = 4AD2 - 4AB2 [1]


Now, In ΔABC, again By Pythagoras theorem


AC2 = AB2 + BC2


AC2 = AB2 + 4AD2 - 4AB2 [From 1]


AC2 = 4AD2 - 3AB2


Hence Proved !

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