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Question

In triangle ABC,B=90 and D is the mid-point of side Be. Prove that :
AC2=AD2+3CD2

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Solution

In ΔABC,
AB2+BC2=AC2
as [BC=2CD]
AB2+4CD2=AC2 --(1)
In ΔABD,
AD2=AB2+BD2=AB2+CD2 --(2)

Subtracting (1) and (2)
AC2AD2=AB2+4CD2(AB2+CD2)AC2AD2=3CD2AC2=AD2+3CD2

Hence proved.

469108_187921_ans_5d0c53add23c458099c8156725082ab0.png

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