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)



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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