in an isosceles triangle ABC AC=AB and D is a point on side BC then prove that. AB^2-AD^2=BD×CD
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Given - AB =AC
To Prove -AB^2-AD^2=BD.CD - (1)
Const. -Join AD
In ABD :
AB^2-AD^2=BD^2 (PYTHAGORAS THEOREM)
since AD is the perpendicular bisector of BC
therefore, BD=CD
putting this value in eq (1)
AB^2-AD^2=BD.BD
AB^2-AD^2=BD.CD ( since BD=CD)
To Prove -AB^2-AD^2=BD.CD - (1)
Const. -Join AD
In ABD :
AB^2-AD^2=BD^2 (PYTHAGORAS THEOREM)
since AD is the perpendicular bisector of BC
therefore, BD=CD
putting this value in eq (1)
AB^2-AD^2=BD.BD
AB^2-AD^2=BD.CD ( since BD=CD)
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