Proof: According to cosine theorem, AB 2+BD 2-AD 2 = 2AB * BD * COSB.

So AB 2-AD 2 = 2AB * BD * COSB-BD2 = BD * (2AB * COSB-BD). ( 1)

As the high AE of triangle ABC, BE=AB*cosB. Because it is an isosceles triangle, BC=2BE.

So BC=2AB*cosB.

Substituting the formula (1), we can get AB 2-AD 2 = 2ab * BD * COSB-BD 2 = BD * (BC-BD) = BD * DC.

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