ABC is a isosceles triangle in which AB=AC
BD Perpendicular to AC
In △ABD
AB2=AD2+BD2 ...(Pythagoras theoram)
∴AC2=AD2+BD2 ....(as AB=AC) ...(1)
From diagram, we see that
⇒AC=CD+AD
⇒AC2=(CD+AD)2
From (1) we get,
⇒(CD+AD)2=AD2+BD2
CD2+AD2+2(CD×AD)=AD2+BD2
CD2+2(CD×AD)=BD2 ...(AD square gets cancelled from both sides)
BD2−CD2=2(CD×AD)
Hence proved.