∴∠D=∠ABD，

∫∠CAB =∠D+∠ABD = 2∠D，

∫∠CAB = 2∠ABC，

∴∠D=∠ABC, and ∠C=∠C,

∴△ABC∽△BDC，

∴ bccd = acbc, that is, ab+c = ba.

∴a2-b2=bc.