Question

In a triangle ABC angle BAC = 90 degree and AD is drawn perp. to BC. Prove that AD2 = BD.CD. Prove it using Pythagoras theorem

Answer 1

Given : In a triangle ABC angle BAC = 90 degree and

AD is drawn perp. to BC.

To Find :  Prove that AD2 = BD.CD.  using Pythagoras theorem

Solution:

using Pythagoras theorem

AB² +AC²   = BC²

AB² = AD² + BD²

AC² = AD²  + CD²

BC = BD + CD

=> AD² + BD² +   AD²  + CD²  = (BD+ CD)²

=>  2AD² + BD² + CD² = BD² + CD² + 2BD.CD

=> 2AD²  = 2BD.CD

=> AD²  =  BD.CD

QED

Hence Proved

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