Question

triangle ABC is right angled at B and D is the midpoint of BC. prove that AC^2=4AD^2-3AB^2

Answer 1

 AC2 = AB2+BC2_(P.T) _ (1)

AD2 = AB2 +BD2 _(P.T)

AD2 = AB2 +1/2BC2

AD2 =AB2 + 1/4BC2

Taking L.C.M

4AD2 =4AB2 +BC2 -(2)

First equation

AC2 = AB2 +BC2

BC2 =AC2 -AB2 -(3)

Substituting (3) in

4AD2 =4AB2 +BC2

4AD2 =4AB2 + (AC2 - AB2)

4AD2 = 3AB2 +AC2

4AD2 -3AB2 =AC2

AC2 =4AD2 -3AB2

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