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\(CD\) and \(GH\) are respectively the bisectors of \(\angle ACB\) and \(\angle EGF\) such that \(D\) and \(H\) lie on sides \(AB\) and \(FE\) of \(\Delta ABC\) and \(\Delta EFG\) respectively. If \(\Delta ABC \sim \Delta FEG\), show that:
(i) \(\frac{CD}{GH} = \frac{AC}{FG}\)
(ii) \(\Delta DCB \sim \Delta HGE\)
(iii) \(\Delta DCA \sim \Delta HGF\)
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