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ABC is a isosceles triangle in which AB=AC
BD Perpendicular to AC
In △ABD
AB^2 =AD^2 +BD^2 ...(Pythagoras theoram)
∴AC^2 =AD^2 +BD^2....(as AB=AC) ...(1)
From diagram, we see that
⇒AC=CD+AD
⇒AC^2 =(CD+AD)^2
From (1) we get,
⇒(CD+AD)^2=AD^2 +BD^2
CD^2+AD^2 +2(CD×AD)=AD^2 +BD^2
CD^2 +2(CD×AD)=BD^2 ...(AD square gets cancelled from both sides)
BD ^2 −CD^2
=2(CD×AD)
Hence proved.
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