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