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

Fiona 1 year 2021-08-30T21:16:05+00:00 0

Answers ( )

    0
    2021-08-30T21:17:07+00:00

    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

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