##
B

4. In Fig, ABC is a triangle in which Z B=90°,D is midpoint of BC. Prove that

AC2 = AD2+3CD2

Question

B

4. In Fig, ABC is a triangle in which Z B=90°,D is midpoint of BC. Prove that

AC2 = AD2+3CD2

## Answers ( )

Explanation:Given: In △ABC, ∠B = 90° and D is the mid-point of BC.

To Prove: AC2 = AD2 + 3CD2

Proof:

In △ABD,

AD2 = AB2 + BD2

AB2 = AD2 – BD2 …….(i)

In △ABC,

AC2 = AB2 + BC2

AB2 = AC2- BD2 ……..(ii)

Equating (i) and (ii)

AD2 – BD2 = AC2 – BC2

AD2 – BD2 = AC2 – (BD + DC)2

AD2 – BD2 = AC2 – BD2- DC2- 2BDx DC

AD2 = AC2 – DC2 – 2DC2 (DC = BD)

AD2 = AC2 – 3DC2