In right angled triangle ABC,angle B = 90 degree ,'D' is the mid point of BC .prove that AC2=4AD2-3AB2

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Solution

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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Similar questions

A C^{2} = (4 A D^{2} - 3 A B^{2}) .

△ A B C

B

D

B C

A C^{2} = 4 A D^{2} - 3 A B^{2}

∠ C = 90

{A B}^{2} = 4 {A D}^{2} - 3 {A C}^{2}

ABC is a right angled triangle at C. If D is the mid point of BC,prove that AB²=4AD²-3AC²

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