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ABC is a triangle in which AB AC and D is any point in BC. Prove thatAB2-AD2 BD. CDCBSE 2005 |
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Answer» AB^2=AE^2+BE^2------(1)AD^2=AE^2+DE^2------(2)(1)-(2)AB^2-AD^2=AE^2+BE^2-AE^2-DE^2=(BD+DE)^2-DE^2=BD^2+2BD(BE-BD)=2BD.BE-BD^2=BD(2BE-BD)=BD(BC-BD)AB^2-AD^2=BD.CD |
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